Summer Conference

Program

Titles & Abstracts

Plenary Talks

V.Betz. Complex spin systems

Abstract. Many models of quantum statistical mechanics have graphical representations. Examples are the quantum Heisenberg ferromagnet (leading to the random interchange model), or the interacting Bose gas (leading to spatial random permutations). In this talk, I will introduce a framework of complex-valued spins and their graphical representations. These systems do not directly describe a quantum model, but have rather similar features, of which I will describe some. 

Moreover, complex spin systems are quite flexible and can be used to describe many well-studied graphical models such as double dimer and loop O(N) models. I will show that under suitable conditions, a rather clean and general proof of reflection positivity can be achieved, and how it can be used to establish long range order in the corresponding graphical systems. 

L. Fresta. The FBSDE method in Euclidean Quantum Field Theory

Abstract. Stochastic quantisation provides a probabilistic route to the construction of Euclidean quantum field theories by realising interacting measures through suitable stochastic differential equations driven by Gaussian noise. Such representations are not unique, and different choices lead to different analytical frameworks. Forward-backward stochastic differential equations (FBSDEs) provide one such framework, via a multiscale coupling with Gaussian noise, reminiscent of ideas from the Renormalisation Group. The aim of this talk is to give an overview of the FBSDE approach to stochastic quantisation. I will describe the basic mechanism behind the method, explain how it can be used to characterise interacting measures and discuss some of its advantages and limitations compared with more traditional techniques. I will conclude with a brief discussion of current directions and open problems.

C. Gérard. The Euclidean vacuum state for linearized gravity on de Sitter spacetime

Abstract. Abstract:  We will consider in this lecture free quantum fields for linearized gravity on  the de Sitter spacetime $dS^{4}$. We will describe the rigorous construction of the Euclidean vacuum state, obtained from the Euclidean Green's function on the $4$-sphere $S^{4}$. We use the notion of Calderón projectors to recover a quantum state for the Lorentzian theory on de Sitter space. We show that while the state is gauge invariant and Hadamard, it is not positive on the whole of the phase space. We show however that a suitable modification at low energies yields a well-defined Hadamard state on global de Sitter space.

B. Hinrichs. A Probabilistic Approach to Exponential Mixing of Quantum Trajectories

Abstract. Quantum trajectories are stochastic unravelings of the time-evolution in open quantum systems, governed by the Lindblad master equation, e.g., occurring in the theory of indirect measurements or as a simulative tool to study open quantum systems. Whereas the solution to the Lindblad equation converges to its invariant state for large times, the quantum trajectory will approach its invariant measure, a property known as ergodicity or mixing; in finite dimensional systems even exponentially fast in Wasserstein distance. Previous proofs of this fact have inherently employed both the knowledge that the Lindbladian relaxes to equilibrium (exponentially fast) as well as the purification property of the quantum trajectory, going back to the work of Maassen and Kümmerer. In this talk, we discuss a selfcontained stochastic proof for exponential mixing of jump-type quantum trajectories, which might also be applied to infinite dimensional systems in which exponential mixing can not be expected for arbitrary initial states. The talk is based on joint work with Martin Kolb and Achim Wübker.

M. Hoshino. Fernique-type Bounds for BPHZ Models and their Applications

Abstract. For general locally subcritical parabolic singular SPDEs without variance blow-up, we prove that the BPHZ model satisfies a Fernique-type theorem, namely exponential square integrability, whenever the driving noise is stationary and satisfies a suitable transportation cost inequality. As applications, we obtain two consequences. First, if the SPDE admits appropriate a priori estimates, then its solution satisfies a corresponding concentration inequality. Second, we show that the BPHZ model satisfies a Schilder-type large deviation principle, and that the solution to the SPDE satisfies a Freidlin-Wentzell-type large deviation principle, extending the result of Hairer and Weber (2015).

This talk is based on a joint work with Ismael Bailleul (Université de Bretagne Occidentale) and Ryoji Takano (Tokyo Metropolitan University).

I. Jauslin. The Simplified approach to the Bose gas

Abstract. Much attention has been given to systems of interacting Bosons in the dilute regime, where powerful theoretical tools such as Bogolyubov theory give detailed and accurate predictions. In this talk, I will discuss a different approach to studying the ground state of Boson systems, which Carlen, Lieb and I have recently found to be accurate at all densities. In particular, it allows us to probe the system in the intermediate density regime, which had, until now, only been accessible to costly Monte-Carlo simulations. In this talk, I will first give an overview of this Simplified approach, and will discuss evidence for non-perturbative behavior in the intermediate density regime obtained using this tool. This is joint work with E. Carlen, and E.H. Lieb.

S. Kusuoka. Properties of the quantum fields constructed by the rotation-invariant approximation

Abstract. In this talk, we consider the properties of the quantum fields constructed by the rotation-invariant approximation and the singular SPDE method. The singular SPDE method enables us to take the limits of the continuous approximation sequences, and we apply the advantage of the continuous approximations. The properties are included in the axioms of the Euclidean quantum field theories, and in particular the regularity property (which is also called the temperedness or the distribution property) and the reflection positivity. We also give a remark on the singularity of the three-dimensional $\Phi ^4$-measure with respect to the free field.

This talk is based mainly on joint works with Sergio Albeverio.

J. Schach Møller. On a signature calculus for resolvent expansions

Abstract. In this talk we consider a resummation scheme for the Neumann expansion of interacting resolvents in quantum field theory, with a view towards constructing ultraviolet renormalized Hamiltonians. The basic idea goes back to Eckmann and Hepp, but we develop the method to allow for higher-order counter-terms of arbitrary order in the coupling. We exemplify the scheme first for the solvable van Hove model for one scalar boson field and subsequently for an interacting model of one fermion field and one boson field without particle conservation.

The talk is based on joint work with Benjamin Alvarez, Toulon.

Y. Ogata. An operator algebraic approach to mixed state topological order

Abstract. The classification of mixed-state topological order requires indices that behave monotonically under finite-depth quantum channels. In two dimensions, a braided C∗-tensor category, which corresponds to strong symmetry, arises from a state satisfying approximate Haag duality. I would like to explain that the S-matrix and topological twists of the braided C∗-tensor category are quantities that are monotone under finite-depth quantum channels.

A. Panati. Entropic fluctuations in quantum two-time measurement framework with direct or indirect (ancilla coupling) protocol

Abstract. Non-equilibrium statistical mechanics has seen some impressive developments in the last three decades, since the ground-breaking formulation of the transient and steady entropic Fluctuation Relations (FR) in the early nineties. The extension of these results to the quantum setting has turned out to be surprisingly challenging and it is still an ongoing sort. Kurchan and Hal Tasaki's seminal works (2000) showed quantum formulation of the transient version of FR is possible by introducing the two-time measurement framework. In this talk, we present some results in a recent series of papers, where we attempt to introduce a quantum equivalent of steady entropic functional and compare it to the transient version for open quantum system. In order to deal with the thermodynamic limit and to have general results, we use methods of C^∗- algebras and modular theory. We will consider idealised direct projective measurement on the reservoirs. We show in particular that the direct measurement has an invasive role, leading to dramatic consequences about stability with respect to the initial state. Therefore it is natural to consider experimentally accessible indirect measurement through coupling with an ancilla. In this context, a parallel with the classical case is restored, but we can prove robustness of the protocol with respect to the first measurement time. Joint work with T. Benoist, L. Bruneau, V. Jaksic, C.A. Pillet.

N. Pinamonti. Equilibrium states for non relativistic bosons and the Gross-Pitaevskii regime

Abstract. In this seminar we present the construction of equilibrium states at finite temperature for weakly interacting non-relativistic bosons with a non-trivial background field in infinitely extended space. Utilizing the framework introduced by Araki and further expanded by Fredenhagen and Lindner, we derive the generating function of the correlation functions of the theory as a suitable series. A Hubbard-Stratonovich transformation is then employed to reformulate this quantity, enabling the analysis of the convergence of the associated loop vertex expansion within specific intermediate regimes. We isolate the tree diagrams that produce the scattering length in the dispersion relations of the two-point function of the state within the Gross-Pitaevskii regime. This scattering length is then used to renormalize both the background and the fluctuation two-point functions, concluding with a discussion about the bounds satisfied by the remainder. Joint work with S. Galanda.

K. Rejzner. Semilocal quantum physics: results and perspectives

Abstract. In this talk I will present the recent developments in semilocal quantum physics, which describes relativized (or relational) observables in quantum theory, in the presence of a quantum reference frame. Starting from a net of local algebras described by algebraic quantum field theory (AQFT), one couples it to a quantum reference frame, which is needed, for example, in the operational description of the measurement theory in the presence of symmetries. Physically, such observables are often non-local, but arise from relativization of local observables.

I. Sasaki. TBA

Abstract. TBA.

M. Wrochna. Zeta renormalization in Minkowski signature

Abstract. In time-dependent settings or on curved spacetimes it is particularly useful to renormalize non-linear field quantities directly in spacetime rather than at the level of a fixed reference time. In Euclidean signature, an extremely successful scheme is the zeta renormalization, so far however it has not been implemented in the Lorentzian setting literally in the operator-theoretic sense, even though local reinterpretations have been proved to be consistent with the Euclidean point of view. In this talk I will present various recent advances (among others based on collaborations/work in progress with C. Gérard, A. Vasy, N.V. Dang, M. Molodyk, E. D’Angelo) that provide the techniques to make zeta renormalization a reality and discuss some consequences.

Contributed Talks

M. Baraniewicz. Smoothing on $L^1$ for ground state transformed Schrödinger semigroups

Abstract. I will speak about the $L^1$-smoothing properties for a broad class of semigroups arising from the ground state transformation of Schrödinger semigroups with confining potentials, associated with non-local Lévy operators, for which (asymptotic) ultracontractivity and hypercontractivity fail. Our work is inspired by Talagrand’s convolution conjecture in the discrete cube setting, as well as by subsequent developments on the classical Ornstein–Uhlenbeck semigroup.  The estimates we provide exhibit a clear dependence on the potential and the Lévy measure defining the kinetic term operator, and they yield a description of the semigroups’ action on $L^1$ in terms of Orlicz spaces. Our framework is quite general, encompassing fractional and relativistic Laplacians as kinetic operators.

X. Chen. On the Second Order Energy Formulas of Quantum Gases

Abstract. We survey the history and the concurrent progress of the mathematical proof of the Bosonic Lee-Huang-Yang and the Fermionic Huang-Yang 2nd order energy formulas of quantum gases. We discuss the recent advancement of the proof of the Huang-Yang formula for Fermions.

D. R. Dolai. Central limit theorem for trace functional of the IDS of magnetic random Schrödinger operators

Abstract. In this work, we consider the magnetic random Schrödinger operator H ω := (i∇ + A)2 + V ω on L2 (Rd ), where A ∈ (L2loc (Rd ))d is a vector potential of a constant magnetic field. We establish Gaussian fluctuations for trace functionals associated with the integrated density of states (IDS). The existence of the IDS is well known in the literature and can be characterized by the limit lim L→∞ (1/|Λ_L |) Tr f (H^ω_Λ_L ,X ) = E[Tr(χ_Λ_1 f (H^ω ) χ_Λ_1 )] for a.e. ω, ∀ f ∈ Cc (R), where H^ω_Λ_L ,X denotes the restriction of H_ω to the cube Λ_L = (− L/2 , L/2 )^d with boundary condition X ∈ {D, N } (Dirichlet or Neumann). This convergence can be interpreted as a law of large numbers (LLN) for the sequence of random variables {Tr(f (HΛωL ,X ))}L . Here, we prove a central limit theorem (CLT) for this sequence when the test function f is once differentiable and decays at infinity at the rate |x|−m with m > d + 1. The limiting variance is independent of the boundary condition X = D, N . Moreover, we provide conditions on the test function f ensuring that the variance is strictly positive.

M. Fantechi. Existence of Solutions for Time-dependent Fractional Kohn-sham Equations

Abstract. We consider time-dependent Kohn-Sham equations in dimension $3$ with a fractional dispersion relation $(1-\Delta)^s$, $s\in(0,\frac32)$, and a class of interaction terms including, in particular, external potentials, internal potentials associated to Hartree-type non-linearities, and exchange terms described by energy subcritical pure-power non-linearities. We prove the local existence of weak solutions in $H^s$ using an approximation procedure regularizing the non-linearities. Assuming that the interaction energies can be controlled by the kinetic energy, we show that the solutions can be extended to global solutions using energy estimates. If $s\in[1,\frac32)$, we establish in addition the well-posedness of the time-dependent Kohn-Sham equations using Strichartz estimates.

D. Fröhlich. A Feynman Path Integral for the Unitary Dynamics of the Spin-Boson Model

Abstract. Path integrals formulated in terms of stochastic processes are typically used to describe the (imaginary-time) semigroup, generated by the Hamiltonian of a quantum mechanical system. By contrast, giving a rigorous meaning to the real-time path integral associated with the unitary time evolution for physically relevant interactions remains a long-standing open problem in mathematical physics. In this talk, I will focus on the spin–boson model, which describes a two-level system linearly coupled to a quantized radiation field. While comparatively elementary, it already exhibits non-trivial features of an interacting quantum field theory and has therefore become a widely studied model in mathematical physics. I will show how the discrete nature of the two-level system can be exploited to construct an operator-valued stochastic process on Fock space that provides a representation of the model's unitary time evolution operator.

R. Gautier. Measuring a quantum system with a semiclassical device

Abstract. In this work in collaboration with M.Falconi and C.Fermanian Kammerer, we study an explicit example of a quantum system coupled with a semiclassical measurement device that undergoes a quantum-to-classical transition, and overcomes the measurement problem. I will first present the standard measurement schemes as introduced in the early days in quantum mechanics, then will explain how our system can be quantitatively described using superadiabatic projectors. Finally I will show that in the semiclassical limit and at macroscopic time, the system reproduces what is expected from a sharp, projective measurement process.

D. Kim. On the semiclassical limit of the Schrödinger-Lohe model and concentration estimates

Abstract. We study the semiclassical limit of the quantum synchronization model and concentration estimates for the resulting limit model. From the Schrödinger-Lohe model, we rigorously derive the Vlasov-Lohe model using the Wigner transform and Wigner measure method. In semiclassical limit, generalized Wigner distributions to the Schrödinger-Lohe model converge to a set of Wigner measures which corresponds to a weak solution to the Vlasov-Lohe model, and then we show the asymptotic collective behaviors of the Vlasov-Lohe model. When one-body potentials are identical, we show that complete synchronization emerges for the Vlasov-Lohe model. In contrast, for non-identical potentials the lack of boundedness results in practical synchronization for the integrals of solutions. Moreover, we construct a global existence of classical solutions to the Vlasov-Lohe model using the standard method of characteristics. Analysis in this work can deal with possibly non-identical potentials in which their differences are constant. This talk is based on joint work [1].

[1] Ha, S.-Y., Hwang, G. and Kim, D.: On the semiclassical limit of the Schr ̈odinger-Lohe model and concentration estimates. J. Math. Phys. 65 (2024), 122702. 

J. Kruse. Scattering Theory and Asymptotic Completeness: From Many-Body Quantum Systems to Quantum Field Theory - The Galilean-Invariant Lee Model

Abstract. The goal of scattering theory is to describe the asymptotic evolution of systems of interacting particles. A central concept in this framework is asymptotic completeness, which asserts that every state can be decomposed into bound and scattering states. While this property is well understood for many-body quantum mechanical systems, asymptotic completeness in quantum field theory remains a difficult open problem. In this talk, I will review the scattering theory of quantum mechanical systems and explain how key ideas from quantum mechanics can be adapted to the study of asymptotic completeness in quantum field theory. In quantum mechanics, asymptotic completeness has been established under fairly general conditions. I will outline essential analytic tools, such as propagation estimates and the convergence of the asymptotic velocity, and their role in proving asymptotic completeness.

M. Lathwood. Defects in Finite-Gauge TQFT and Enumerative Invariants from Symmetric Groups

Abstract. We study topological quantum field theories with finite gauge group from the perspective of defects and enumerative geometry. Starting from Dijkgraaf–Witten theory, viewed as a finite-group analogue of Chern–Simons theory, we reinterpret partition functions on punctured surfaces and their products with the circle as weighted counts of flat bundles, or equivalently of group homomorphisms from fundamental groups into symmetric groups. For gauge group Sn, we show that the Dijkgraaf–Witten partition function on a punctured sphere times a circle reproduces the unitary invariants appearing in matrix and tensor models, and admits a natural expression as a sum over classical Hurwitz numbers counting branched covers of the sphere. We then introduce a defect version of Dijkgraaf–Witten theory, where holonomies are constrained to lie in specified subgroups along codimension-one defect curves. In the case of defects associated to the wreath product Sn[S2] ⊂ S2n, the resulting defect partition functions compute orthogonal invariants and admit an interpretation in terms of wreath Hurwitz numbers. More generally, we construct mixed unitar-orthogonal invariants as defect partition functions associated to relative (H, K)-bundles, and propose a corresponding notion of UO-Hurwitz numbers counting constrained factorizations in symmetric groups. Our results provide a unifying TQFT framework for unitary, orthogonal, and mixed UO-invariants, clarifying their relationship to branched coverings, symmetric-group combinatorics, and defect structures in finite-gauge topological field theories.

C. Lejsek. Operator Theoretic Renormalization of the Standard Model of the non-relativistic QED

Abstract. In this talk, I will show that the ground state of the Standard Model of non-relativistic qed depends analytically on the coupling constant and the dilation parameter without requiring an infrared cutoff. I will first give a brief overview of previous work on this topic and then introduce the generalized Pauli-Fierz transformation, the smooth Feshbach map and the renormalization transformation. Using these concepts, we can apply the operator theoretic renormalization introduced in Smooth Feshbach map and operator-theoretic renormalization group methods by Bach, Chen, Fröhlich and Sigal and show the analyticity of the transformed operator in the coupling constant and dilation parameter. The final result is obtained using arguments of elliptic regularity and the properties of analytic vectors. This is joint work with D. Hasler.

G. Lipardi. Spin-wave theory for 3D quantum XY model

Abstract. The low-temperature behavior of spin systems with a continuous symmetry is expected to be governed by Gaussian fluctuations around the ground state, known as spin waves. For classical models this picture has been rigorously established by Bricmont–Fontaine–Lebowitz–Lieb–Spencer (1982) for the O(2) model and, more recently, by Giuliani–Ott (2025) for general O(N) systems. In the quantum setting, however, the situation is more subtle: the low-energy behavior arises from a nontrivial interplay between thermal and quantum excitations, and a rigorous justification of spin-wave theory, understood as a semiclassical expansion in the spin size S, has remained open. In this talk I will discuss a constructive approach to this problem for the ground state of the three-dimensional quantum XY model. After introducing the Holstein–Primakoff bosonic representation and the resulting quadratic spin-wave approximation, I will explain how multiscale renormalization-group methods can be used to control the infrared divergences arising in the formal large-S expansion. The main result of this construction is a uniform factorial bound on the coefficients of the resulting 1/S expansion for the zero-temperature spontaneous magnetization. This is based on joint work with S. Cenatiempo (GSSI) and A. Giuliani (Roma Tre).

D.T. Nguyen. 2D rotating Bose-Einstein condensation at the critical rotation speed

Abstract. We study the minimizers of a magnetic 2D non-linear Schrödinger energy functional in a harmonic trapping potential, describing a rotating Bose-Einstein condensate. In the case of a repulsive interaction potential, we derive an effective Thomas-Fermi-like model in the rapidly rotating limit where the centrifugal force compensates the confinement. The available states are restricted to the lowest Landau level. The coupling constant of the Thomas-Fermi functional is to link the emergence of vortex lattices (the Abrikosov problem). When turning from repulsive to attractive interactions, the system is unstable since there is a balance between kinetic and interaction energies. In the regime where the strength of the interaction approaches a critical value from below, the system collapses to a profile obtained from the (unique) optimizer of a Gagliardo-Nirenberg interpolation inequality. This was established before in the case of fixed rotation frequency. We extend the result to rotation frequencies approaching, or even equal to, the critical frequency at which the centrifugal force compensates the trap. We prove that the blow-up scenario is to leading order unaffected by such a strong deconfinement mechanism. In particular, the blow-up profile remains independent of the rotation frequency.

P. Paulovics. Composite observables and nonperturbative Operator Product Expansion via stochastic analysis

Abstract. We begin to develop a framework for the rigorous description of general composite observables in Euclidean quantum field theories. The approach is fully nonperturbative and combines renormalization group ideas with techniques of stochastic analysis. As a proof of concept, we construct various local observables of the sineGordon model on the plane up to the third threshold \beta^2< 6\pi and prove existence of the Operator Product Expansion for them. Based on ongoing work with M. Gubinelli.

M. Peev. Large N Convergence of Matrix SPDEs 

Abstract. The rich field of free probability is based on the describing tracial correlations of collections random matrices as their size tends to infinity. However, most results focus on the behaviour of finitely many independent random matrices and are of an underlying combinatorial nature. We will show how one can envelop these standard results of random matrix theory into an analytic framework that allows us to show the weak and strong convergence of solutions of the \Phi^4_2-equation driven by matrix-valued white noise to the solution of this equation in free probability.

L. Pettinari. Subcritical Temperature Regimes in Lattice Spin Systems

Abstract. Lattice spin systems describe quantum particles whose positions are confined to the vertices of a graph, so that only their internal degrees of freedom contribute to the dynamics. In this talk, I will present new sufficient conditions for identifying a high-temperature regime in which the system exhibits subcritical behaviour. These conditions are formulated in terms of the uniqueness of Kubo–Martin–Schwinger (KMS) states and rely on a non-commutative analogue of the Kirkwood–Salzburg equations, combined with a novel decomposition of local observables. In contrast to standard approaches, our results are uniform in the single-site Hilbert space dimension and require only a bound on the inverse critical temperature that depends on the natural C*-norm of the interaction potentials. I will also discuss the strengths and limitations of this method, as well as potential extensions to systems with infinite-dimensional single-site Hilbert spaces.

(Joint work with N. Drago and C. F. J. van de Ven. Based on arXiv:2511.12651 and Commun. Math. Phys. 406, 163 (2025).)

C.A. Rossi. Semiclassical Analysis with resolvent C*-algebra

Abstract. In this talk, we aim at developing semiclassical analysis on states of the resolvent C*-algebra, introduced in 2008 by D. Buchholz and H. Grundling as a new algebraic framework to encode the CCRs. In light of the large number of quantum dynamics and observables encompassed therein, the resolvent C*-algebra represents a more suitable alternative to the standard Weyl C*-algebra in describing interacting Bosonic systems. After a preliminary comparison between the two aforementioned algebras, we introduce a novel concrete realization of the commutative resolvent C*-algebra. Together with its non-Abelian counterpart, it is used to provide a proper mathematical setting to perform the semiclassical limit of Bosonic quantum states. In this limit, classical resolvent states are interpreted as expectation values of functions belonging to the Abelian resolvent C*-algebra. Hence, they can be recovered from the quantum ones, read as functionals on the non-Abelian resolvent C*-algebra, by sending the semiclassical parameter to zero in a proper topology. From the physical standpoint, the semiclassical limit turns out to be crucial in the mathematical formulation of the Bohr correspondence principle, which makes precise the connection between the classical and the quantum description of a given system. To verify the robustness of this principle, we build quantization maps on suitable subsets of the commutative algebra, obtaining the corresponding quantum observables in the non-Abelian one. Once the quantization procedure has been performed, we define suitable families of states on quantized resolvent observables. In conclusion, we prove the existence, for those nets of quantum states, of at least one classical state for the semiclassical parameter going to zero.

A. Rout. A microscopic derivation of the classical KMS condition in one dimension

Abstract. The Kubo-Martin-Schwinger (KMS) condition characterises the equilibrium states of a quantum system. By formally taking a semiclassical limit, one can formulate a classical KMS condition, which can also characterise the equilibrium states of the corresponding classical system. In this talk, I will discuss how to rigorously take this limit in the context of the one-dimensional interacting Bose gas and a sequence of quantum Gibbs states. The proof is based on semiclassical analysis and the theory of Wigner measures.

Based on joint work with Zied Ammari, Shahnaz Farhat, and Soeren Petrat.

T. Schmidt. Fluctuation bounds for long-range self-interacting path measures

Abstract. In this talk we study probability measures of the form

$$\hat{\mathbb P}_{\alpha,T}(\mathrm d  x) \propto \exp \left( -\alpha \int_0 ^T \mathrm d t \int_0 ^T \mathrm d s \frac{\Vert x_t - x_s \Vert^\gamma}{1+|t-s|^\xi} \right) \mathbb P(\mathrm d x),$$

where $\alpha,\gamma,\xi > 0$ and $\mathbb P$ is Brownian motion. Of interest are upper bounds on the mean-square displacement at time $T$, and its asymptotic behavior. These types of measures arise naturally when studying polaron models from a statistical mechanics point of view.  Moreover, the mean-square displacement is in general closely connected to the effective mass of an electron interacting with a polarizable medium. We present an approach based on the Gaussian correlation inequality that allows us to upper bound the mean-square displacement in terms of $\gamma$ and $\xi$. In particular, we find different regimes of fluctuations, ranging from collapse of the variance to sub-diffusive behavior, up to $\xi <2+ \gamma/2$ in case $\gamma \in (0,2)$. Permitting time, we also discuss lower bounds on the mean-square displacement in case the self-interaction is repulsive (i.e. $\alpha \to - \alpha)$ and $\mathbb P$ is replaced by a random walk.

Joint work with Volker Betz and Mark Sellke.

J. Schober. Outgoing Endomorphism Semigroups of Standard Subspaces

Abstract. Standard subspaces are well-studied objects in the Haag–Kastler axiomatic framework of algebraic quantum field theory. The axiom of isotony motivates the investigation of one-parameter semigroups of unitary endomorphisms of standard subspaces. In this talk, we show how a real version of the classical Lax–Phillips theorem, originally developed in the context of scattering theory, can be used to represent these endomorphism semigroups on an L2-space over the real line. We demonstrate how classical results on standard subspaces, such as Borchers' one-particle theorem and the results of Longo and Witten, translate to the Lax–Phillips framework and how they connect to theorems on Hardy spaces such as the Beurling–Lax theorem.

O. Siebert. Hamiltonian Learning with Continuous Fermions

Abstract. Hamiltonian learning is the process of obtaining or approximating a Hamiltonian through the measurement of certain time-evolved initial states.  In this talk, I will discuss a new approach to learning an external one-body potential through a field of free non-relativistic fermions in continuous space. Unlike earlier lattice-based settings, this approach involves the mathematical challenges of infinite-dimensional Hilbert spaces and unbounded operators, including the propagation of information at an a priori unbounded speed. We present an algorithm that can efficiently reconstruct various classes of physically relevant potentials, including Coulomb potentials. For smooth potentials, we can use recently proven Lieb-Robinson bounds to achieve significant speedups through parallelization.  This is joint work with A. Bluhm, M. Lemm and T. Möbus.

S. Spruck. Effective Dynamics for the Bose Polaron in the Large-Volume Mean-Field Limit

Abstract. We consider the dynamics of the Bose polaron system, a dense quantum gas consisting of $N$ bosons evolving in $\mathbb{R}^3$ in the presence of an impurity particle. The system is studied in the mean-field scaling with initially high density $\rho$ and large volume $\Lambda$ of the gas. In the initial state, almost all bosons are in the Bose-Einstein condensate, with a few excitations. We derive from the microscopic dynamics, in the joint limit of large densities and volumes, with the constraint $\Lambda^3 \ll \rho$, the effective description by the translation-invariant Bogoliubov-Fröhlich Hamiltonian, which couples the quantum field of excitations linearly to the impurity particle.

T. Takaesu. On the binding condition by the decay of particle’s potential

Abstract. The system of a particle interacting with a Bose field is investigated. It is proven that the binding condition holds by the decay of particle’s potential. As an application, the exponential decay of the ground state follows.

R. Toriumi. Invitation to Random Tensor Models: from random geometry, enumeration of tensor invariants, to characteristic polynomials

Abstract. I will introduce random tensor models by first reviewing their motivation coming from random geometric approach to quantum gravity. Then, I will selectively present some of the interesting research results, by highlighting recent results on enumeration of graphs representing tensor invariants, and reporting our recent work on a new notion of characteristic polynomials for tensors via Grassmann integrals and distributions of roots of random tensors. The latter two are based on arXiv:2404.16404[hep-th] and arXiv:2510.04068[math-ph].