Search results for "Imaginary time"

ON THE CALCULATION OF THE HEAT CAPACITY IN PATH INTEGRAL MONTE CARLO SIMULATIONS

1992

In Path Integral Monte Carlo simulations the systems partition function is mapped to an equivalent classical one at the expense of a temperature-dependent Hamiltonian with an additional imaginary time dimension. As a consequence the standard relation linking the heat capacity Cv to the energy fluctuations, <E2>−<E>2, which is useful in standard classical problems with temperature-independent Hamiltonian, becomes invalid. Instead, it gets replaced by the general relation [Formula: see text] for the intensive heat capacity estimator; β being the inverse temperature and the subscript P indicates the P-fold discretization in the imaginary time direction. This heatcapacity estimator…

Corrigendum to “Imaginary time propagation code for large-scale two-dimensional eigenvalue problems in magnetic fields” [Comput. Phys. Comm. 184(3) (…

2016

Fermion sign problem in imaginary-time projection continuum quantum Monte Carlo with local interaction

2016

We use the Shadow Wave Function formalism as a convenient model to study the fermion sign problem affecting all projector Quantum Monte Carlo methods in continuum space. We demonstrate that the efficiency of imaginary time projection algorithms decays exponentially with increasing number of particles and/or imaginary-time propagation. Moreover, we derive an analytical expression that connects the localization of the system with the magnitude of the sign problem, illustrating this prediction through some numerical results. Finally, we discuss the fermion sign problem computational complexity and methods for alleviating its severity.

Nonequilibrium Green's function approach to strongly correlated few-electron quantum dots

2009

The effect of electron-electron scattering on the equilibrium properties of few-electron quantum dots is investigated by means of nonequilibrium Green's function theory. The ground and equilibrium states are self-consistently computed from the Matsubara (imaginary time) Green's function for the spatially inhomogeneous quantum dot system whose constituent charge carriers are treated as spin-polarized. To include correlations, the Dyson equation is solved, starting from a Hartree-Fock reference state, within a conserving (second-order) self-energy approximation where direct and exchange contributions to the electron-electron interaction are included on the same footing. We present results for…

Imaginary time propagation code for large-scale two-dimensional eigenvalue problems in magnetic fields

2013

We present a code for solving the single-particle, time-independent Schr\"odinger equation in two dimensions. Our program utilizes the imaginary time propagation (ITP) algorithm, and it includes the most recent developments in the ITP method: the arbitrary order operator factorization and the exact inclusion of a (possibly very strong) magnetic field. Our program is able to solve thousands of eigenstates of a two-dimensional quantum system in reasonable time with commonly available hardware. The main motivation behind our work is to allow the study of highly excited states and energy spectra of two-dimensional quantum dots and billiard systems with a single versatile code, e.g., in quantum …

Semiadiabatic High-Field Polarization Response in Ferroelectrics I: Hysteresis and Nonlinear Susceptibility

2004

Ginzburg-Landau theory for ferroelectric phase instability is combined with Langevin, Fokker-Planck and imaginary time Schrodinger equation techniques to model impact of thermal noise in the kinetics of ferroelectric polarization. The proposed real space/real time numerical method allows to efficiently simulating relaxation, dynamic hysteresis and general dielectric response.

High Field Polarization Response in Ferroelectrics: Current Solutions and Challenges

2006

Polarization response including ergodicity breaking and the divergence of relaxation time is reproduced for model Hamiltonians of growing complexity. Systematic derivation of the dynamical equations and its solutions is based on the Fokker-Planck and imaginary time Schrödinger equation techniques with subsequent symplectic integration. Test solutions are addressed to finite size and spatially extended problems with microscopically interpretation of the model parameters as a challenge.

Stochastic Dynamics of Ferroelectric Polarization

2008

This study is addressed to the conceptual and technical problems emerging for ferroelectric systems out of thermodynamic equilibrium. The theoretical setup includes a lattice of interacting cells, each cell obeying regular dynamics determined by Ginzburg-Landau model Hamiltonians whereas relaxation toward minimum energy state is reproduced by thermal environment. Representative examples include polarization response of a single lattice cell, birth of a domain as triggered by the ergodicity breaking, and the effect of nonlocal electroelastic interaction all evidenced combining the Fokker-Planck, imaginary time Schrodinger and symplectic integration techniques.

Theory and modeling of polarization switching in ferroelectrics

2005

Abstract Kinetics of polarization response in ferroelectrics is reproduced within Langevin, Fokker–Planck and imaginary time Schrodinger equation techniques for energy functionals of growing complexity modeling an assembly of coarse grained particles with attractive first neighbor interaction. Symplectic integration based numerical approach captures dynamic hysteresis, polarization switching, and spatially extended stationary polarization. Solution of relevant nonstationary problem is adapted to large scale parallel computing.

Hypergestures in Complex Time: Creative Performance Between Symbolic and Physical Reality

2015

Musical performance and composition imply hypergestural transformation from symbolic to physical reality and vice versa. But most scores require movements at infinite physical speed that can only be performed approximately by trained musicians. To formally solve this divide between symbolic notation and physical realization, we introduce complex time (\(\mathbb {C}\)-time) in music. In this way, infinite physical speed is “absorbed” by a finite imaginary speed. Gestures thus comprise thought (in imaginary time) and physical realization (in real time) as a world-sheet motion in space-time, corresponding to ideas from physical string theory. Transformation from imaginary to real time gives us…