Related papers: Fractional exclusion statistics in disordered inte…
Interacting fermion systems in one dimension, which in the low energy approximation are described by Luttinger liquid theory, can be reformulated as systems of weakly interacting particles with fractional exchange statistics. This is shown…
We consider the asymmetric simple exclusion process (ASEP) on a semi-infinite chain which is coupled at the end to a reservoir with a particle density that changes periodically in time. It is shown that the density profile assumes a…
Simulating time evolution is one of the most natural applications of quantum computers and is thus one of the most promising prospects for achieving practical quantum advantage. Here, we develop quantum algorithms to extract thermodynamic…
We develop a continuum limit and mean-field theory for interacting particle systems (IPS) on self-similar networks, a new class of discrete models whose large-scale behavior gives rise to nonlocal evolution equations on fractal domains.…
The behaviour of extended particles with exclusion interaction on a one-dimensional lattice is investigated. The basic model is called $\ell$-ASEP as a generalization of the asymmetric exclusion process (ASEP) to particles of arbitrary…
Non-equilibrium thermodynamics provides a general framework for understanding non-equilibrium processes, particularly in small systems that are typically far from equilibrium and dominated by fluctuations. However, the experimental…
The design of small scale non-equilibrium steady states (NESS) is a challenging, open ended question. While similar equilibrium problems are tractable using standard thermodynamics, a generalized description for non-equilibrium systems is…
This paper deals with the asymptotic behavior and FEM error analysis of a class of strongly damped wave equations using a semidiscrete finite element method in spatial directions combined with a finite difference scheme in the time…
Physical laws governing population dynamics are generally expressed as differential equations. Research in recent decades has incorporated fractional-order (non-integer) derivatives into differential models of natural phenomena, such as…
We study two-component bosonic systems with strong inter-species and vanishing intra-species interactions. A new class of exact eigenstates is found with energies that are {\it not} sums of the single-particle energies with wave functions…
The totally asymmetric simple exclusion process (TASEP) is a well studied example of far-from-equilibrium dynamics. Here, we consider a TASEP with open boundaries but impose a global constraint on the total number of particles. In other…
We study in detail the effect of quasicondensation. We show that this effect is strictly related to dimensionality of the system. It is present in one dimensional systems independently of interactions - exists in repulsive, attractive or in…
This thesis is devoted to the theoretical study of slow thermodynamic processes in non-equilibrium stochastic systems. Its main result is a physically and mathematically consistent construction of relevant thermodynamic quantities in the…
We study a low temperature anisotropic anti-ferromagnetic 2D Ising model through the guise of a certain dimer model. This model has a bijection with a one-dimensional particle system equipped with creation and annihilation. In the…
We formulate a comprehensive theoretical description of excitation harvesting in molecular aggregates photoexcited by weak incoherent radiation. An efficient numerical scheme that respects the continuity equation for excitation fluxes is…
A physical system exposes to us in a real space, while its description often refers to its reciprocal momentum space. A connection between them can be established by exploring patterns of quasiparticles interference (QPI), which is…
In this paper, we compute stiffness matrix of the nonlocal Laplacian discretized by the piecewise linear finite element on nonuniform meshes, and implement the FEM in the Fourier transformed domain. We derive useful integral expressions of…
We consider the problem of filtering dynamical systems, possibly stochastic, using observations of statistics. Thus, the computational task is to estimate a time-evolving density $\rho(v, t)$ given noisy observations of the true density…
The relaxation to equilibrium in many systems which show strange kinetics is described by fractional Fokker-Planck equations (FFPEs). These can be considered as phenomenological equations of linear nonequilibrium theory. We show that the…
Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite…