Related papers: The Quantum Liouville Equation for the Effective A…
We consider a natural dimension reduction technique for the Liouville-von Neumann equation for a mixed quantum system based on evaluation of a trace formula combined with a direct expansion in modified Chebyshev polynomials. This reduction…
By using the Lewis-Riesenfeld theory and the invariant-related unitary transformation formulation, the exact solutions of the {\it time-dependent} Schr\"{o}dinger equations which govern the various Lie-algebraic quantum systems in atomic…
The problem of response of nonequilibrium systems is currently under intense investigation. We propose a general method of solution of the Liouville Equation for thermostatted particle systems subjected to external forces which retains only…
Determining the dynamics of interacting integrable many-particle quantum systems at finite times after homogeneous quantum quenches is a long-standing challenge. We present a Monte Carlo sampling scheme that numerically evaluates the…
A general scheme is presented for controlling quantum systems using evolution driven by non-selective von Neumann measurements, with or without an additional tailored electromagnetic field. As an example, a 2-level quantum system controlled…
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the particle coordinate and momentum dispersions are derived. A new…
There is a sub-class of the solutions to Quantum Tetrahedron Equation related to the algebraical Pentagon Equation. The Quantum Tetrahedron Equation defines an evolution operator in wholly discrete three dimensional space-time. In this…
A scale--dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow. It is invariant under general coordinate transformations and satisfies…
By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to…
This note starts with a recapitulation of what people call the ``Measurement Problem'' of Quantum Mechanics (QM). The dissipative nature of the quantum-mechanical time-evolution of averages of states over large ensembles of identical…
The interaction between two parts in a compound quantum system may be reconsidered more completely than before and some new understandings and conclusions different from current quantum mechanics are obtained, including the conservation law…
We introduce the concept of interpolation in quantum evolution and present a general framework to find the energy optimal Hamiltonian for a quantum system evolving among a given set of middle states using variational and geometric methods.…
In this paper we present a new quantum-trajectory based treatment of quantum dynamics suitable for dissipative systems. Starting from a de Broglie/Bohm-like representation of the quantum density matrix, we derive and define quantum…
We introduce a quantum version of the Game of Life and we use it to study the emergence of complexity in a quantum world. We show that the quantum evolution displays signatures of complex behaviour similar to the classical one, however a…
The evolution of mixed states of a closed quantum system is described by a group of evolution superoperators whose infinitesimal generator (the quantum Liouville superoperator, or Liouvillian) determines the mixed-state counterpart of the…
We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic…
An exact evolution equation, the functional generalization of the Callan-Symanzik method, is given for the effective action of QED where the electron mass is used to turn the quantum fluctuations on gradually. The usual renormalization…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
We carefully analyse the use of the effective action in dynamical problems, in particular the conditions under which the equation $\frac{\delta \Ga} {\delta \phi}=0$ can be used as a quantum equation of motion, and the relation between the…