Related papers: The Quantum Liouville Equation for the Effective A…
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level…
An exact differential equation is derived for the evolution of the Liouville effective action with the mass parameter. This derivation is based on properties of the exponential potential and some consequences of the equation are discussed.
This second part deals with applications of a general method to describe the quantum time evolution determined by a Schroedinger equation with time-dependent Hamiltonian. A new aspect of our approach is that we find all solutions starting…
The wide-spread opinion is that original quantum mechanics is a reversible theory, but this statement is only true for undecomposed systems, that are those systems which sub-systems are out of consideration. Taking sub-systems into account,…
We present a numerical method to simulate the time evolution, according to a Hamiltonian made of local interactions, of quantum spin chains and systems alike. The efficiency of the scheme depends on the amount of the entanglement involved…
The correct quantum description for a curvature squared term in the action can be obtained by casting the action in the canonical form with the introduction of a variable which is the negative of the first derivative of the field variable…
We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this…
In these lecture notes we discuss recent progress in the rigorous derivation of effective evolution equations for the description of the dynamics of quantum mechanical many-body systems.
By analyzing the relationships between a socioeconomical system modeled through evolutionary game theory and a physical system modeled through quantum mechanics we show how although both systems are described through two theories apparently…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
We study the time evolution of correlation functions in closed quantum systems for nonequilibrium ensembles of initial conditions. For a scalar quantum field theory we show that generic time-reversal invariant evolutions approach…
We study nonequilibrium evolution in a self-interacting quantum field theory invariant under space translation only by using a canonical approach based on the recently developed Liouville-von Neumann formalism. The method is first used to…
We discuss a new analytical approach to real-time evolution in quantum many-body systems. Our approach extends the framework of continuous unitary transformations such that it amounts to a novel solution method for the Heisenberg equations…
Quantum Liouville theory is analyzed in terms of the infinite dimensional representations of $U_Qsl(2,C)$ with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining…
A consistent classical and quantum relativistic mechanics can be constructed if Einstein's covariant time is considered as a dynamical variable. The evolution of a system is then parametrized by a universal invariant identified with…
Quantum simulation using time evolution in phase estimation-based quantum algorithms can yield unbiased solutions of classically intractable models. However, long runtimes open such algorithms to decoherence. We show how measurement-based…
We present a nonperturbative field theoretic method based on the Liouville-Neumann (LN) equation. The LN approach provides a unified formulation of nonperturbative quantum fields and also nonequilibrium quantum fields, which makes use of…
Description of time evolution of the relativistic unstable electromagnetic system consisting of Fermi-Dirac particle interacting with electromagnetic field, in the framework of the Liouville space extension of quantum mechanics is done. The…