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This note provides an introduction to molecular dynamics, the computational implementation of the theory of statistical physics. The discussion is focused on the properties of Langevin dynamics, a degenerate stochastic differential equation…
After a short review of one of proposals to avoid complex stochastic processes in Complex Langevin studies, the recent progress in the former is reported. In particular, the new developments allow now to construct positive and normalizable…
Stochastic hybrid systems involve a coupling between a discrete Markov chain and a continuous stochastic process. If the latter evolves deterministically between jumps in the discrete state, then the system reduces to a piecewise…
A method is developed which speeds up averaging in quantum simulations where minus signs cause difficulties. A Langevin equation method in conjunction with a replication algorithm is used enabling one to average over a continuously varying…
At finite density, lattice simulations are hindered by the well-known sign problem: for finite chemical potentials, the QCD action becomes complex and the Boltzmann weight $e^{-S}$ cannot be interpreted as a probability distribution to…
A linear open quantum system consisting of a harmonic oscillator linearly coupled to an infinite set of independent harmonic oscillators is considered; these oscillators have a general spectral density function and are initially in a…
We study one-dimensional functional inequalities of the type of Poincar\'e, logarithmic Sobolev and Wirtinger, with weight, for probability densities with polynomial tails. As main examples, we obtain sharp inequalities satisfied by inverse…
We investigate piecewise-linear stochastic models as with regards to the probability distribution of functionals of the stochastic processes, a question which occurs frequently in large deviation theory. The functionals that we are looking…
Previous years researchers began to simulate open quantum system, taking into account the interaction between system and the environment. One approach to deal with this problem is to use the density matrix within the Liouville-von-Neumann…
For the characterization of surface height profiles we present a new stochastic approach which is based on the theory of Markov processes. With this analysis we achieve a characterization of the complexity of the surface roughness by means…
I review the presence of the sign problem in lattice QCD at nonzero baryon density and its relation with the overlap and Silver Blaze problems. I then discuss progress in some cases where the sign problem can be handled, either because the…
Quantum field theories (QFTs) at finite densities of matter generically involve complex actions. Standard Monte-Carlo simulations based upon importance sampling, which have been producing quantitative first principle results in particle…
Simulations of full QCD at nonzero baryon density using light quark masses are presented. The sign problem is evaded by the usage of the complex Langevin equation. The simulations are stabilized by the gauge cooling procedure for small…
The three-dimensional SU(3) spin model is an effective Polyakov loop model for QCD at nonzero temperature and density. It suffers from a sign problem at nonzero chemical potential. We revisit this model using complex Langevin dynamics and…
The complex Langevin method, a numerical method used to compute the ensemble average with a complex partition function, often suffers from runaway instability. We study the regularization of the complex Langevin method via augmenting the…
Presentation of the probability as an intrinsic property of the nature leads researchers to switch from deterministic to stochastic description of the phenomena. The procedure of stochastization of one-step process was formulated. It allows…
A formulation of Langevin dynamics for discrete systems is derived as a class of generic stochastic processes. The dynamics simplify for a two-state system and suggest a network architecture which is implemented by the Langevin machine. The…
We study the Stephanov model, which is an RMT model for QCD at finite density, using the Complex Langevin algorithm. Naive implementation of the algorithm shows convergence towards the phase quenched or quenched theory rather than to…
Given a discrete stochastic process, for example a chemical reaction system or a birth and death process, we often want to find a continuous stochastic approximation so that the techniques of stochastic differential equations may be brought…
This paper studies the limitations of the generic approaches to solving cryptographic problems in classical and quantum settings in various models. - In the classical generic group model (GGM), we find simple alternative proofs for the…