Related papers: A BBGKY-like Hierarchy for Quantum Field Theories
The performance of computational methods for many-body physics and chemistry is strongly dependent on the choice of basis used to cast the problem; hence, the search for better bases and similarity transformations is important for progress…
We present an approach to solving the evolution of a classical $N$-particle ensemble based on the path integral approach to classical mechanics. This formulation provides a perturbative solution to the Liouville equation in terms of a…
In classical kinetic theory, the BBGKY hierarchy is an infinite chain of integro-differential equations that describes the full time-reversal-invariant (Liouville) system of interacting (quasi)-particles in terms of $N$-particle…
We consider the motion of interacting particles governed by a coupled system of ODEs with random initial conditions. Direct computations for such systems are prohibitively expensive due to a very large number of particles and randomness…
Fast and efficient numerical-analytical approach is proposed for modeling complex collective behaviour in accelerator/plasma physics models based on BBGKY hierarchy of kinetic equations. Our calculations are based on variational and…
Mitigation of quantum errors is critical for current NISQ devices. In the present work, we address this task by treating the execution of quantum algorithms as the time evolution of an idealized physical system. We use knowledge of its…
In this work, we analyze the Born, Bogoliubov, Green, Kirkwood and Yvon (BBGKY) hierarchy of equations for describing the full time-evolution of a many-body fermionic system in terms of its reduced density matrices (at all orders). We…
The aim of this work is to study the properties of groups of operators for evolution equations of quantum many-particle systems, namely, the von Neumann hierarchy for correlation operators, the BBGKY hierarchy for marginal density operators…
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between non-degenerate instantaneous eigen-energy levels in such a…
To set up a self-consistent quantum field theory of degenerate systems, the unperturbed state should be described by a density matrix instead of a pure state. This increases the combinatorial complexity of the many-body equations. Hopf…
Recently Mazenko and Das and Mazenko introduced a non-equilibrium field theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual…
We study the growth of correlations in systems with weak long-range interactions. Starting from the BBGKY hierarchy, we determine the evolution of the two-body correlation function by using an expansion of the solutions of the hierarchy in…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
We develop a rigorous formalism for the description of the evolution of states of quantum many-particle systems in terms of a one-particle density operator. For initial states which are specified in terms of a one-particle density operator…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
This paper extends the formalism for quantizing field theories via a microcanonical quantum field theory and Hamilton's principle to classical evolution equations. These are based on the well-known correspondence under a Wick rotation…
A generalization of the Gibbs-von Neumann relative entropy is proposed based on the quantum BBGKY [Bogolyubov-Born-Green-Kirkwood-Yvon] hierarchy as the nonequilibrium entropy for an N-body system. By using a generalization of the…
We consider a class of spinless-fermion Lindblad equations that exhibit decoupled BBGKY hierarchies. In the cases where particle number is conserved, their late time behaviour is characterized by diffusive dynamics, leading to an infinite…
A new form of quasiclassical space-time dynamics for constrained systems reveals how quantum effects can be derived systematically from canonical quantization of gravitational systems. These quasiclassical methods lead to additional fields,…
Recently, the one particle quantum mechanics has been obtained in the framework of an entirely classical subquantum kinetics. In the present paper we argue that, within the same scheme and without any additional assumption, it is possible…