physics

Physics

http://en.wikipedia.org/wiki/Stochastic_differential_equation

http://en.wikipedia.org/wiki/Stochastic_process

http://en.wikipedia.org/wiki/Stochastic_resonance

http://en.wikipedia.org/wiki/Random_matrix

http://en.wikipedia.org/wiki/Mean_field

Brownian motion

http://en.wikipedia.org/wiki/Random_walk#Random_walk_on_graphs

http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.0240v2.pdf

http://ocw.mit.edu/OcwWeb/Mathematics/18-366Fall-2006/LectureNotes/index.htm

Brownian rachets http://en.wikipedia.org/wiki/Brownian_ratchet

Feynman Lectures in Physics (Addison-Wesley, Reading, MA), Vol. 1, Chapter 46.

As described originally by Smoluchowski and noted by Feynman a Brownian particle can undergo net transport on a potential energy surface that is externally driven to fluctuate between several distinct states. Brownian ratchets have attracted theoretical attention because of their description of molecular motors and their similarity with phenomena termed stochastic resonance and resonance activation

Brownian ratchets have been demonstrated to transport micrometer-to millimeter-sized particles in experiments with ratchets generated by dielectrophoresis, optical tweezers, and electrocapillary forces

http://en.wikipedia.org/wiki/Brownian_motor

Langevin equation (from Wikipedia): http://en.wikipedia.org/wiki/Langevin_equation

In statistical physics, a Langevin equation is a stochastic differential equation describing Brownian motion in a potential.

The first Langevin equations to be studied were those in which the potential is constant, so that the acceleration a of a Brownian particle of mass m is expressed as the sum of a viscous force which is proportional to the particles velocity v (Stokes' law), a noise term

(the name given in physical contexts to terms in stochastic differential equations which are stochastic processes) representing the effect of a continuous series of collisions with the atoms of the underlying fluid and F(x) which is the systematic interaction force due to the intramolecular and intermolecular interactions:

Essentially similar equations govern other Brownian systems, such as thermal noise in an electrical resistor:

Many interesting results can often be obtained without solving the Langevin equation, from the fluctuation dissipation theorem.

The main method of solution if a solution is required is by use of the Fokker-Planck equation, which provides a deterministic equation satisfied by the time dependent probability density. Alternatively numerical solutions can be obtained by Monte Carlo simulation. Other techniques, such as path integration have also been used, drawing on the analogy between statistical physics and quantum mechanics (for example the Fokker-Planck equation can be transformed into the Schrödinger equation by rescaling a few variables).

Ising model http://en.wikipedia.org/wiki/Ising_model

Fokker-Plank

http://en.wikipedia.org/wiki/Stochastic_differential_equation

http://en.wikipedia.org/wiki/Fokker-Planck_equation

Fokker-Plank in Finance market:

http://en.wikipedia.org/wiki/Stochastic_Volatility

http://www.emis.de/journals/SIGMA/2008/038/sigma08-038.pdf

Perlocation

Resistance Of Unlimited Grid

http://arxiv.org/abs/cond-mat/9909120v1

http://arxiv.org/abs/cond-mat/9909120v4

http://www.physics.thetangentbundle.net/wiki/Analog_circuits/infinite_resistive_lattice

Unsorted

Лагранжиан и гамильтониан получаются друг из друга преобразованием Лежандра (для выпуклых функций). Поэтому если гамильтониан имеет физический смысл (энергия), то и лагранжиан тоже.

переход к комплексному времени и соответствие классической статфизики евклидовым квантам впечатляющий трюк.

Кстати, есть ли в этом более глубокий смысл, по-моему, до сих пор не известно.