Related papers: Exact BCS stochastic schemes for a time dependent …
Biochemical systems are inherently stochastic, particularly those with small-molecule populations. The spatial distribution of molecules plays a critical role and requires the inclusion of spatial coordinates in their analysis. Stochastic…
We review progress towards direct simulation of quantum dynamics in many-body systems, using recently developed stochastic gauge techniques. We consider master equations, canonical ensemble calculations and reversible quantum dynamics are…
We construct many-body scar states in multi-flavour fermionic lattice models that possess strong magnetic or superconducting correlations of a given type specified by a unitary matrix $A$. One of the states maximizes the one-point…
Recently Wang and Cheng proposed a self-consistent effective Hamiltonian theory (SCEHT) for many-body fermionic systems (Wang & Cheng, 2019). This paper attempts to provide a mathematical foundation to the formulation of the SCEHT that…
In this paper we derive for a controlled stochastic evolution system on a Hilbert space sufficient conditions for optimality. Our result is derived by using its so-called adjoint backward stochastic evolution equation.
This paper is concerned with providing the maximum principle for a control problem governed by a stochastic evolution system on a separable Hilbert space. In particular, necessary conditions for optimality for this stochastic optimal…
The exact solution of the 1D interacting mixed Bose-Fermi gas is used to calculate ground-state properties both for finite systems and in the thermodynamic limit. The quasimomentum distribution, ground-state energy and generalized…
We perform a variational quantum Monte Carlo simulation of an interacting Fermi gas confined in a three dimensional harmonic potential. This gas is considered as the precursor system from which a molecular bosonic gas is formed. Based on…
The primary work presented in this paper focuses on the calculation of density-density dynamical correlations in an attractive two dimensional Fermi gas in several physically interesting regimes, including the strongly correlated BEC-BCS…
We study the time evolution of the amount of entanglement generated by one dimensional spin-1/2 Ising-type Hamiltonians composed of many-body interactions. We investigate sets of states randomly selected during the time evolution generated…
We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady…
We consider a two-component Fermi gas with a contact interaction from the BCS regime to the unitary limit. Starting from the idea that many-body effects should not depend on short-distance or high-momentum physics which is encoded in the…
The dynamics of strongly interacting trapped dilute Fermi gases (dilute in the sense that the range of interatomic potential is small compared with inter-particle spacing) is investigated in a single-equation approach to the time-dependent…
In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…
We develop a pairing mean-field theory to describe the quantum dynamics of the dissociation of molecular Bose-Einstein condensates into their constituent bosonic or fermionic atoms. We apply the theory to one, two, and three-dimensional…
We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective…
We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as…
We investigate strongly correlated many-body systems composed of bosons and fermions with a fully quantum treatment using the path-integral ground state method, PIGS. To account for the Fermi-Dirac statistics, we implement the fixed-node…
We calculate the time evolution of a far-from-equilibrium initial state of a non-relativistic ultracold Bose gas in one spatial dimension. The non-perturbative approximation scheme is based on a systematic expansion of the two-particle…
This paper examines the temporal evolution of a two-stage stochastic model for spherical random fields. The model uses a time-fractional stochastic hyperbolic diffusion equation, which describes the evolution of spherical random fields on…