Related papers: Phase space representation of quantum dynamics
Interacting spin systems are of fundamental relevance in different areas of physics, as well as in quantum information science, and biology. These spin models represent the simplest, yet not fully understood, manifestation of quantum…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
An approach to the quantum-classical mechanics of phase space dependent operators, which has been proposed recently, is remodeled as a formalism for wave fields. Such wave fields obey a system of coupled non-linear equations that can be…
We discuss an ab initio world-line approach to constructing phase space distributions in systems with internal symmetries. Starting from the Schwinger-Keldysh real time path integral in quantum field theory, we derive the most general…
We show that classicality emerges during quantum phase transitions due to parametric interactions without coupling to environments. The Wigner functions are explicitly calculated for the Gaussian vacuum, number, and thermal states of a free…
The necessity and utility of considering the interaction of a quantum system with its environment when describing its time evolution have been recognized in several branches of physics and of other sciences. The Kraus' representation is a…
We develop an approach to quantum dynamics based on quantum phase space trajectories. The latter are built from a unitary irreducible representation of the symmetry group of the respective classical phase space. We use a quantum action…
One of the key conceptual challenges in quantum gravity is to understand how quantum theory should modify the very notion of spacetime. One way to investigate this question is to study the alternatives to Schr\"odinger quantum mechanics.…
We present a quantum theory of the shuttle instability in electronic transport through a nanostructure with a mechanical degree of freedom. A phase space formulation in terms of the Wigner function allows us to identify a cross-over from…
We present a framework for simulating the open dynamics of spin-boson systems by combining variational non-Gaussian states with a quantum trajectories approach. We apply this method to a generic spin-boson Hamiltonian that has both…
In this article we try to bridge the gap between the quantum dynamical semigroup and Wigner function approaches to quantum open systems. In particular we study stationary states and the long time asymptotics for the quantum Fokker-Planck…
We present a general method by which linear quantum Hamiltonian dynamics with exponentially many degrees of freedom is replaced by approximate classical nonlinear dynamics with the number of degrees of freedom (phase space dimensionality)…
We introduce dynamical versions of loop (or Dyson-Schwinger) equations for large families of two--dimensional interacting particle systems, including Dyson Brownian motion, Nonintersecting Bernoulli/Poisson random walks, $\beta$--corners…
A formulation of quantum-classical hybrid dynamics is presented, which concerns the direct coupling of classical and quantum mechanical degrees of freedom. It is of interest for applications in quantum mechanical approximation schemes and…
An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one dimensional chaotic dynamical systems. Environmental fluctuations -- characteristic of all realistic dynamical systems -- suppress…
Understanding real-time dynamics of interacting quantum fields in curved spacetime remains a major theoretical challenge. We employ tensor network methods to study such dynamics using interacting scalar and gauge theories in 1+1 spacetime…
There are no phase-space trajectories for anharmonic quantum systems, but Wigner's phase-space representation of quantum mechanics features Wigner current~$\bf J$. This current reveals fine details of quantum dynamics -- finer than is…
We study monitored quantum dynamics of infinite-range interacting bosonic systems in the thermodynamic limit. We show that under semiclassical assumptions, the quantum fluctuations along single monitored trajectories adopt a deterministic…
Simulation of conditional master equations is important to describe systems under continuous measurement and for the design of control strategies in quantum systems. For large bosonic systems, such as BEC and atom lasers, full quantum field…
We show that the dynamical Wigner functions for noninteracting fermions and bosons can have complex singularity structures with a number of new solutions accompanying the usual mass-shell dispersion relations. These new shell solutions are…