Related papers: Statistical Field Theory of Interacting Nambu Dyna…
We develop a Hamilton-Jacobi-like formulation of Nambu mechanics. The Nambu mechanics, originally proposed by Nambu more than four decades ago, provides a remarkable extension of the standard Hamilton equations of motion in even dimensional…
In the context of non-relativistic quantum field theory, a method is proposed for multiplying field operators at the same spatial point and obtaining regular (i.e. rigorously defined) interaction terms for the Hamiltonian. The basic idea is…
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…
Taking as a model the fact that Heisenberg's matrix mechanics was derived from Hamiltonian mechanics using the correspondence principle, we explore a class of dynamical systems involving discrete variables, with Nambu mechanics as the…
Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. Here we extend this technique and use it to…
Classical Hamiltonian mechanics, characterized by a single conserved Hamiltonian (energy) and symplectic geometry, `hides' other invariants into symmetries of the Hamiltonian or into the kernel of the Poisson tensor. Nambu mechanics aims to…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description of field theories, and the conformal character has been…
We propose a variant formulation of Hamiltonian systems by the use of variables including redundant degrees of freedom. We show that Hamiltonian systems can be described by extended dynamics whose master equation is the Nambu equation or…
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…
Open quantum systems play a central role in contemporary nanoscale technologies, including molecular electronics, quantum heat engines, quantum computation and information processing. A major theoretical challenge is to construct dynamical…
We present a theoretical framework and a calculational scheme to study the coexistence and competition of thermodynamic phases in quantum statistical mechanics. The crux of the method is the realization that the microscopic Hamiltonian,…
We show that the dynamical symmetry exists in dissipative quantum many-body systems. Under constraints on both Hamiltonian and dissipation parts, the time evolution of particular observables can be symmetric between repulsive and attractive…
Systems with long range interactions display some anomalies when its dynamics and thermodynamics are studied below certain conditions. Among these anomalies are the quasi- stationary states, which are exacerbated because of special initial…
In this work we revisit the problem of equilibration in isolated many-body interacting quantum systems. We pay particular attention to quantum chaotic Hamiltonians, and rather than focusing on the properties of the asymptotic states and how…
We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving…
An analytical method to compute thermodynamic properties of a given Hamiltonian system is proposed. This method combines ideas of both dynamical systems and ensemble approaches to thermodynamics, providing de facto a possible alternative to…
It is understood that in free bosonic theories, the classical field theory accurately describes the full quantum theory when the occupancy numbers of systems are very large. However, the situation is less understood in interacting theories,…
We study the d-HMF model proposed by Atenas and Curilef, a mean field model with long-range interactions inspired by the dipole-dipole interaction. Among the challenges of this thesis is: the resolution of the d-HMF model in the canonical…
The Hamiltonian Mean-Field model has been investigated, since its introduction about a decade ago, to study the equilibrium and dynamical properties of long-range interacting systems. Here we study the long-time behavior of long-lived,…