90,815 research outputs found
From Classical to Quantum and Back: Hamiltonian Adaptive Resolution Path Integral, Ring Polymer, and Centroid Molecular Dynamics
Path integral-based simulation methodologies play a crucial role for the
investigation of nuclear quantum effects by means of computer simulations.
However, these techniques are significantly more demanding than corresponding
classical simulations. To reduce this numerical effort, we recently proposed a
method, based on a rigorous Hamiltonian formulation, which restricts the
quantum modeling to a small but relevant spatial region within a larger
reservoir where particles are treated classically. In this work, we extend this
idea and show how it can be implemented along with state-of-the-art path
integral simulation techniques, such as ring polymer and centroid molecular
dynamics, which allow the approximate calculation of both quantum statistical
and quantum dynamical properties. To this end, we derive a new integration
algorithm which also makes use of multiple time-stepping. The scheme is
validated via adaptive classical--path-integral simulations of liquid water.
Potential applications of the proposed multiresolution method are diverse and
include efficient quantum simulations of interfaces as well as complex
biomolecular systems such as membranes and proteins
Quantum Mechanics by Numerical Simulation of Path Integral
Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2017, Tutor: Federico MesciaThe Quantum Mechanics formulation of Feynman is based on the concept of path integrals, allowing to express the quantum transition between two space-time points without using the bra and ket formalism in the Hilbert space. A particular advantage of this approach is the ability to provide an intuitive representation of the classical limit of Quantum Mechanics. The practical importance of path integral formalism is being a powerful tool to solve quantum problems where the analytic solution of the Schrödinger equation is unknown. For this last type of physical systems, the path integrals can be calculated with the help of numerical integration methods suitable for implementation on a computer. Thus, they provide the development of arbitrarily accurate solutions. This is particularly important for the numerical simulation of strong interactions (QCD) which cannot be solved by a perturbative treatment. This thesis will focus on numerical techniques
to calculate path integral on some physical systems of interest
Computer Simulation of Quantum Dynamics in a Classical Spin Environment
In this paper a formalism for studying the dynamics of quantum systems
coupled to classical spin environments is reviewed. The theory is based on
generalized antisymmetric brackets and naturally predicts open-path
off-diagonal geometric phases in the evolution of the density matrix. It is
shown that such geometric phases must also be considered in the
quantum-classical Liouville equation for a classical bath with canonical phase
space coordinates; this occurs whenever the adiabatics basis is complex (as in
the case of a magnetic field coupled to the quantum subsystem). When the
quantum subsystem is weakly coupled to the spin environment, non-adiabatic
transitions can be neglected and one can construct an effective non-Markovian
computer simulation scheme for open quantum system dynamics in classical spin
environments. In order to tackle this case, integration algorithms based on the
symmetric Trotter factorization of the classical-like spin propagator are
derived. Such algorithms are applied to a model comprising a quantum two-level
system coupled to a single classical spin in an external magnetic field.
Starting from an excited state, the population difference and the coherences of
this two-state model are simulated in time while the dynamics of the classical
spin is monitored in detail. It is the author's opinion that the numerical
evidence provided in this paper is a first step toward developing the
simulation of quantum dynamics in classical spin environments into an effective
tool. In turn, the ability to simulate such a dynamics can have a positive
impact on various fields, among which, for example, nano-science.Comment: To appear in Theoretical Chemistry Accounts (special issue in honor
of Professor Gregory Sion Ezra
Semiclassical Universe from First Principles
Causal Dynamical Triangulations in four dimensions provide a
background-independent definition of the sum over space-time geometries in
nonperturbative quantum gravity. We show that the macroscopic four-dimensional
world which emerges in the Euclidean sector of this theory is a bounce which
satisfies a semiclassical equation. After integrating out all degrees of
freedom except for a global scale factor, we obtain the ground state wave
function of the universe as a function of this scale factor.Comment: 15 pages, 4 figure
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