Search results for "quantum dynamics"
showing 10 items of 127 documents
Semiquantum molecular dynamics simulation of thermal properties and heat transport in low-dimensional nanostructures
2012
We present a detailed description of the semi-quantum approach to the molecular dynamics simulation of stochastic dynamics of a system of interacting particles. Within this approach, the dynamics of the system is described with the use of classical Newtonian equations of motion in which the quantum effects are introduced through random Langevin-like forces with a specific power spectral density (the color noise). The color noise describes the interaction of the molecular system with the thermostat. We apply this technique to the simulation of the thermal properties of different low-dimensional nanostructures. Within this approach, we simulate the specific heat and heat transport in carbon n…
Many-body quantum dynamics by adiabatic path-integral molecular dynamics: Disordered Frenkel Kontorova models
2005
The spectral density of quantum mechanical Frenkel Kontorova chains moving in disordered, external potentials is investigated by means of path-integral molecular dynamics. If the second moment of the embedding potential is well defined (roughness exponent ), there is one regime in which the chain is pinned (large masses of chain particles) and one in which it is unpinned (small ). If the embedding potential can be classified as a random walk on large length scales ( ), then the chain is always pinned irrespective of the value of . For , two phonon-like branches appear in the spectra.
Quantum bubble dynamics in the presence of gravity
1991
Abstract The dynamics of spherical quantum bubbles in 3+1 dimensions is governed by a Klein-Gordon-type equation which simulates the quantum mechanical motion of a relativistic point particle in 1+1 dimensions. This dimensional reduction is especially clear in the minisuperspace formulation first used in quantum cosmology and adapted here to quantum bubble dynamics. The payoff of this formulation is the discovery of the gravitational analogue of the Klein effect, namely the crossing of positive and negative energy levels of the particle spectrum induced by an external gravitational field. This phenomenon gives rise to a finite probability that a vacuum bubble might tunnel from an initial bo…
The Usefulness of Lie Brackets: From Classical and Quantum Mechanics to Quantum Electrodynamics
2020
We know that in Hamiltonian systems a dynamic function f(q, p) develops in time according to
Simulating open quantum systems with trapped ions
2005
This paper focuses on the possibility of simulating the open system dynamics of a paradigmatic model, namely the damped harmonic oscillator, with single trapped ions. The key idea consists in using a controllable physical system, i.e. a single trapped ion interacting with an engineered reservoir, to simulate the dynamics of other open systems usually difficult to study. The exact dynamics of the damped harmonic oscillator under very general conditions is firstly derived. Some peculiar characteristic of the system’s dynamics are then presented. Finally a way to implement with trapped ion the specific quantum simulator of interest is discussed.
Quantum Solitons on Quantum Chaos: Coherent Structures, Anyons, and Statistical Mechanics
1991
This paper is concerned with the exact evaluation of functional integrals for the partition function Z (free energy F = -β -1 ln Z, β -1 = temperature) for integrable models like the quantum and classical sine-Gordon (s-G) models in 1+1 dimensions.1–12 These models have wide applications in physics and are generic (and important) in that sense. The classical s-G model in 1+1 dimensions $${\phi _{xx}} - {\phi _{tt}} = {m^2}\sin \phi$$ (1) (m > 0 is a “mass”) has soliton (kink, anti-kink and breather) solutions. In Refs 1–12 we have reported a general theory of ‘soliton statistical mechanics’ (soliton SM) in which the particle description can be seen in terms of ‘solitons’ and ‘phonons’. The …
Fundamental Principles of Quantum Mechanics
2001
There are two alternative methods of quantizing a system: a) quantization via the Feynman Path Integral (equivalent to Schwinger’s Action Principle); b) canonical quantization.
Reply to Comment on Measurement of quantum states of neutrons in the Earth's gravitational field
2003
Physical review / D 68(10), 108702 (2003). doi:10.1103/PhysRevD.68.108702
Quantum Mechanics of Point Particles
2013
In developing quantum mechanics of pointlike particles one is faced with a curious, almost paradoxical situation: One seeks a more general theory which takes proper account of Planck’s quantum of action \(h\) and which encompasses classical mechanics, in the limit \(h\rightarrow 0\), but for which initially one has no more than the formal framework of canonical mechanics. This is to say, slightly exaggerating, that one tries to guess a theory for the hydrogen atom and for scattering of electrons by extrapolation from the laws of celestial mechanics. That this adventure eventually is successful rests on both phenomenological and on theoretical grounds.
A pedagogical approach to the Magnus expansion
2010
Time-dependent perturbation theory as a tool to compute approximate solutions of the Schrodinger equation does not preserve unitarity. Here we present, in a simple way, how the Magnus expansion (also known as exponential perturbation theory) provides such unitary approximate solutions. The purpose is to illustrate the importance and consequences of such a property. We suggest that the Magnus expansion may be introduced to students in advanced courses of quantum mechanics.