Related papers: Effective Evolution Equations from Quantum Dynamic…
Recent experiments have demonstrated single-site resolved observation of cold atoms in optical lattices. Thus, in the future it may be possible to take repeated snapshots of an interacting quantum many-body system during the course of its…
In this article, we consider a set of trial wave-functions denoted by $| Q \right>$ and an associated set of operators $A_\alpha$ which generate transformations connecting those trial states. Using variational principles, we show that we…
We propose an approximate solution of the time-dependent Schr\"odinger equation using the method of stationary states combined with a variational matrix method for finding the energies and eigenstates. We illustrate the effectiveness of the…
Quantum-classical molecular dynamics, as a partial classical limit of the full quantum Schr\"odinger equation, is a widely used framework for quantum molecular dynamics. The underlying equations are nonlinear in nature, containing a quantum…
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…
Ever since the advent of quantum mechanics, it has been clear that the atoms composing matter do not obey Newton's laws. Instead, their behavior is described by the Schroedinger equation. Surprisingly though, until recently, no clear…
In the geometry of quantum-mechanical processes, the time-varying curvature coefficient of a quantum evolution is specified by the magnitude squared of the covariant derivative of the tangent vector to the state vector. In particular, the…
Rules of quantization and equations of motion for a finite-dimensional formulation of Quantum Field Theory are proposed which fulfill the following properties: a) both the rules of quantization and the equations of motion are covariant; b)…
We enhance our quantitative comprehension of the complexity associated with both time-optimal and time sub-optimal quantum Hamiltonian evolutions that connect arbitrary source and target states on the Bloch sphere, as recently presented in…
We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of the…
The energy-based stochastic extension of the Schrodinger equation is a rather special nonlinear stochastic differential equation on Hilbert space, involving a single free parameter, that has been shown to be very useful for modelling the…
We construct a descriptive toy model that considers quantum effects on biological evolution starting from Chaitin's classical framework. There are smart evolution scenarios in which a quantum world is as favorable as classical worlds for…
Quantum mechanics predicts that unobserved systems may exist in a superposition of states, yet measurement produces definite outcomes, a tension at the heart of the quantum-to-classical boundary. How the transformation between these…
In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This…
The dynamics of a quantum system following a sudden, highly non-adiabatic change of its control parameter (quantum quench) is studied with quasiclassical techniques. Recent works have shown, using exact quantum mechanical approach, that…
The dynamics of quantum phase transitions poses one of the most challenging problems in modern many-body physics. Here, we study a prototypical example in a clean and well-controlled ultracold atom setup by observing the emergence of…
The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part…
A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schrodinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an…
The level of current understanding of the physics of time-dependent strongly correlated quantum systems is far from complete, principally due to the lack of effective controlled approaches. Recently, there has been progress in the…
A fast and stable numerical method is formulated to compute the time evolution of a wave function in a magnetic field by solving the time-dependent Schroedinger equation. This computational method is based on the finite element method in…