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One of our research interests revolves around the Casimir effect, which is an effect originally proposed by Hendrik B. G. Casimir in 1948 for a system containing two parallel, perfectly conducting but electrically neutral plates, bathed in a sea of electromagnetic waves. Owing to Dirichlet boundary conditions imposed by the plates, the zero-point fluctuation modes of the electromagnetic field confined between the plates have to be standing waves whose wavelengths are constrained by the separation distance between the plates. On the other hand, the zero-point modes of the electromagnetic field to the exterior of the plates occur in a vastly larger vacuum, so their wavelengths are not “discretized”; correspondingly, there are more such unconfined fluctuating modes than there are confined ones. Thus, there is a “Casimir pressure” which pushes the two plates towards each other, arising as an “osmotic” pressure due to the imbalance of the confined and unconfined modes.
One of our research interests revolves around the Casimir effect, which is an effect originally proposed by Hendrik B. G. Casimir in 1948 for a system containing two parallel, perfectly conducting but electrically neutral plates, bathed in a sea of electromagnetic waves. Owing to Dirichlet boundary conditions imposed by the plates, the zero-point fluctuation modes of the electromagnetic field confined between the plates have to be standing waves whose wavelengths are constrained by the separation distance between the plates. On the other hand, the zero-point modes of the electromagnetic field to the exterior of the plates occur in a vastly larger vacuum, so their wavelengths are not “discretized”; correspondingly, there are more such unconfined fluctuating modes than there are confined ones. Thus, there is a “Casimir pressure” which pushes the two plates towards each other, arising as an “osmotic” pressure due to the imbalance of the confined and unconfined modes.
The reality of the Casimir pressure has been confirmed by modern precision experiments. For small interseparation distances the Casimir force is also known as the van der Waals force, and for finite temperatures it is more generally known as the Casimir-Lifshitz force. The Casimir effect has practical consequences, accounting for the ability of geckos to stick to walls and leading to stiction and non-contact friction in micro- and nanoelectromechanical systems (MEMS and NEMS). Main objectives for our research in this domain include studying the nature and character of Casimir force and friction, for example how repulsive Casimir forces can emerge in topological systems, and the applications of such forces to real systems such as optomechanical devices and trapping of ultracold atoms.
The reality of the Casimir pressure has been confirmed by modern precision experiments. For small interseparation distances the Casimir force is also known as the van der Waals force, and for finite temperatures it is more generally known as the Casimir-Lifshitz force. The Casimir effect has practical consequences, accounting for the ability of geckos to stick to walls and leading to stiction and non-contact friction in micro- and nanoelectromechanical systems (MEMS and NEMS). Main objectives for our research in this domain include studying the nature and character of Casimir force and friction, for example how repulsive Casimir forces can emerge in topological systems, and the applications of such forces to real systems such as optomechanical devices and trapping of ultracold atoms.
Casimir/van der Waals forces between a pair of dielectrically similar surfaces tend to be attractive. However, they can become repulsive if the surfaces break electromagnetic reciprocity, which colloquially speaking is Newton’s Third Law applied to the context of electromagnetism, i.e., the work done on a source by the field induced by a second source is equal to the work done on the second source by the field induced by the first source. This reciprocity would be broken if time reversal symmetry-breaking (TRSB) effects are present, such as those due to an external magnetic field or the magnetization on the surface. Examples include magnetic topological insulators and surfaces that exhibit the quantum anomalous Hall effect. Indeed, Casimir repulsion was predicted to occur for a pair of TRSB topological insulator slabs by Adolfo Grushin and Alberto Cortijo in 2011.
Casimir/van der Waals forces between a pair of dielectrically similar surfaces tend to be attractive. However, they can become repulsive if the surfaces break electromagnetic reciprocity, which colloquially speaking is Newton’s Third Law applied to the context of electromagnetism, i.e., the work done on a source by the field induced by a second source is equal to the work done on the second source by the field induced by the first source. This reciprocity would be broken if time reversal symmetry-breaking (TRSB) effects are present, such as those due to an external magnetic field or the magnetization on the surface. Examples include magnetic topological insulators and surfaces that exhibit the quantum anomalous Hall effect. Indeed, Casimir repulsion was predicted to occur for a pair of TRSB topological insulator slabs by Adolfo Grushin and Alberto Cortijo in 2011.
We have examined the issue of dielectric anisotropy in TRSB topological insulators for the case of uniaxial anisotropy, and found that the thermal Casimir force can also be tuned from attraction to repulsion via the rotation of the optic axis of one TRSB topological insulator relative to that of the other. This (which can be of relevance to the design of MEMS/NEMS with “anti-stictive” properties) is described in more detail in the paper: B.-S. Lu, “van der Waals torque and force between anisotropic topological insulator slabs.” Physical Review B 97, 045427 (2018).
We have examined the issue of dielectric anisotropy in TRSB topological insulators for the case of uniaxial anisotropy, and found that the thermal Casimir force can also be tuned from attraction to repulsion via the rotation of the optic axis of one TRSB topological insulator relative to that of the other. This (which can be of relevance to the design of MEMS/NEMS with “anti-stictive” properties) is described in more detail in the paper: B.-S. Lu, “van der Waals torque and force between anisotropic topological insulator slabs.” Physical Review B 97, 045427 (2018).
Besides the Casimir effect, we are also interested in problems from soft condensed matter, typically those which involve the interplay of boundaries, fluctuations and biology. An example of such a problem is the interaction between “in vivo” cell membranes in the biological environment. The problem is a complicated one, but the expectation is that the interaction between “in vitro” biomimetic membranes (such as dipalmitoylphosphatidylglycerol (DPPG) bilayers) in a salt solution would provide a reasonable first approximation. The canonical theory for the osmotic pressure between fluid membranes was proposed by Wolfgang Helfrich in 1978. It has been usual to account for the effect of electrostatic and van der Waals forces in the solution by simply adding these forces to the Helfrich force between fluid membranes, similar to what has been done in the DLVO theory.
Besides the Casimir effect, we are also interested in problems from soft condensed matter, typically those which involve the interplay of boundaries, fluctuations and biology. An example of such a problem is the interaction between “in vivo” cell membranes in the biological environment. The problem is a complicated one, but the expectation is that the interaction between “in vitro” biomimetic membranes (such as dipalmitoylphosphatidylglycerol (DPPG) bilayers) in a salt solution would provide a reasonable first approximation. The canonical theory for the osmotic pressure between fluid membranes was proposed by Wolfgang Helfrich in 1978. It has been usual to account for the effect of electrostatic and van der Waals forces in the solution by simply adding these forces to the Helfrich force between fluid membranes, similar to what has been done in the DLVO theory.
In reality, fluctuation forces are not additive. The issue of non-additivity can be addressed via a variational framework, for example, a Feynman-Kleinert type variational theory, which can self-consistently account for the contribution of the bending fluctuations of the membrane as well as other fluctuation forces (e.g., electrostatic and van der Waals). Three novel results then emerge from such an analysis.
In reality, fluctuation forces are not additive. The issue of non-additivity can be addressed via a variational framework, for example, a Feynman-Kleinert type variational theory, which can self-consistently account for the contribution of the bending fluctuations of the membrane as well as other fluctuation forces (e.g., electrostatic and van der Waals). Three novel results then emerge from such an analysis.
Firstly, besides bending fluctuations, the “zero mode” fluctuations (i.e., the positional fluctuations of the “centre of mass”) of the membrane also contribute to the osmotic pressure. Secondly, an analytic expression accounting for steric effects can be obtained from a suitable saddle point approximation on the steric constraint imposed on the partition function. Thirdly, in problems involving charged membranes in electrolyte solutions, there is the question of a proper electrostatic boundary condition. In this respect, by looking at the sign of the Hessian, the variational scheme enables one to identify the more physically consistent boundary condition.
Firstly, besides bending fluctuations, the “zero mode” fluctuations (i.e., the positional fluctuations of the “centre of mass”) of the membrane also contribute to the osmotic pressure. Secondly, an analytic expression accounting for steric effects can be obtained from a suitable saddle point approximation on the steric constraint imposed on the partition function. Thirdly, in problems involving charged membranes in electrolyte solutions, there is the question of a proper electrostatic boundary condition. In this respect, by looking at the sign of the Hessian, the variational scheme enables one to identify the more physically consistent boundary condition.
The foregoing approach has been successfully applied to explain the results of a small-angle X-ray scattering experiment performed on biomimetic DPPG vesicles in NaCl salt solution, and is more fully described in the papers: B.-S. Lu, S. P. Gupta, M. Belicka, R. Podgornik and G. Pabst. “Modulation of elasticity and interactions in charged lipid multibilayers by monovalent salt.” Langmuir 32, 13546 (2016) and B.-S. Lu and R. Podgornik. “Effective interactions between fluid membranes.” Physical Review E 92, 022112 (2015).
The foregoing approach has been successfully applied to explain the results of a small-angle X-ray scattering experiment performed on biomimetic DPPG vesicles in NaCl salt solution, and is more fully described in the papers: B.-S. Lu, S. P. Gupta, M. Belicka, R. Podgornik and G. Pabst. “Modulation of elasticity and interactions in charged lipid multibilayers by monovalent salt.” Langmuir 32, 13546 (2016) and B.-S. Lu and R. Podgornik. “Effective interactions between fluid membranes.” Physical Review E 92, 022112 (2015).
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