236 research outputs found
Introduction to Configuration Path Integral Monte Carlo
In low-temperature high-density plasmas quantum effects of the electrons are
becoming increasingly important. This requires the development of new
theoretical and computational tools. Quantum Monte Carlo methods are among the
most successful approaches to first-principle simulations of many-body quantum
systems. In this chapter we present a recently developed method---the
configuration path integral Monte Carlo (CPIMC) method for moderately coupled,
highly degenerate fermions at finite temperatures. It is based on the second
quantization representation of the -particle density operator in a basis of
(anti-)symmetrized -particle states (configurations of occupation numbers)
and allows to tread arbitrary pair interactions in a continuous space.
We give a detailed description of the method and discuss the application to
electrons or, more generally, Coulomb-interacting fermions. As a test case we
consider a few quantum particles in a one-dimensional harmonic trap. Depending
on the coupling parameter (ratio of the interaction energy to kinetic energy),
the method strongly reduces the sign problem as compared to direct path
integral Monte Carlo (DPIMC) simulations in the regime of strong degeneracy
which is of particular importance for dense matter in laser plasmas or compact
stars. In order to provide a self-contained introduction, the chapter includes
a short introduction to Metropolis Monte Carlo methods and the second
quantization of quantum mechanics.Comment: chapter in book "Introduction to Complex Plasmas: Scientific
Challenges and Technological Opportunities", Michael Bonitz, K. Becker, J.
Lopez and H. Thomsen (Eds.) Springer Series "Atomic, Optical and Plasma
Physics", vol. 82, Springer 2014, pp. 153-194 ISBN: 978-3-319-05436-0 (Print)
978-3-319-05437-7 (Online
Coupled coarse graining and Markov Chain Monte Carlo for lattice systems
We propose an efficient Markov Chain Monte Carlo method for sampling
equilibrium distributions for stochastic lattice models, capable of handling
correctly long and short-range particle interactions. The proposed method is a
Metropolis-type algorithm with the proposal probability transition matrix based
on the coarse-grained approximating measures introduced in a series of works of
M. Katsoulakis, A. Majda, D. Vlachos and P. Plechac, L. Rey-Bellet and
D.Tsagkarogiannis,. We prove that the proposed algorithm reduces the
computational cost due to energy differences and has comparable mixing
properties with the classical microscopic Metropolis algorithm, controlled by
the level of coarsening and reconstruction procedure. The properties and
effectiveness of the algorithm are demonstrated with an exactly solvable
example of a one dimensional Ising-type model, comparing efficiency of the
single spin-flip Metropolis dynamics and the proposed coupled Metropolis
algorithm.Comment: 20 pages, 4 figure
Non-Fermi-liquid d-wave metal phase of strongly interacting electrons
Developing a theoretical framework for conducting electronic fluids
qualitatively distinct from those described by Landau's Fermi-liquid theory is
of central importance to many outstanding problems in condensed matter physics.
One such problem is that, above the transition temperature and near optimal
doping, high-transition-temperature copper-oxide superconductors exhibit
`strange metal' behaviour that is inconsistent with being a traditional Landau
Fermi liquid. Indeed, a microscopic theory of a strange-metal quantum phase
could shed new light on the interesting low-temperature behaviour in the
pseudogap regime and on the d-wave superconductor itself. Here we present a
theory for a specific example of a strange metal---the 'd-wave metal'. Using
variational wavefunctions, gauge theoretic arguments, and ultimately
large-scale density matrix renormalization group calculations, we show that
this remarkable quantum phase is the ground state of a reasonable microscopic
Hamiltonian---the usual t-J model with electron kinetic energy and two-spin
exchange supplemented with a frustrated electron `ring-exchange' term,
which we here examine extensively on the square lattice two-leg ladder. These
findings constitute an explicit theoretical example of a genuine
non-Fermi-liquid metal existing as the ground state of a realistic model.Comment: 22 pages, 12 figures: 6 pages, 7 figures of main text + 16 pages, 5
figures of Supplementary Information; this is approximately the version
published in Nature, minus various subedits in the main tex
Three applications of path integrals: equilibrium and kinetic isotope effects, and the temperature dependence of the rate constant of the [1,5] sigmatropic hydrogen shift in (Z)-1,3-pentadiene
Recent experiments have confirmed the importance of nuclear quantum effects
even in large biomolecules at physiological temperature. Here we describe how
the path integral formalism can be used to describe rigorously the nuclear
quantum effects on equilibrium and kinetic properties of molecules.
Specifically, we explain how path integrals can be employed to evaluate the
equilibrium (EIE) and kinetic (KIE) isotope effects, and the temperature
dependence of the rate constant. The methodology is applied to the [1,5]
sigmatropic hydrogen shift in pentadiene. Both the KIE and the temperature
dependence of the rate constant confirm the importance of tunneling and other
nuclear quantum effects as well as of the anharmonicity of the potential energy
surface. Moreover, previous results on the KIE were improved by using a
combination of a high level electronic structure calculation within the
harmonic approximation with a path integral anharmonicity correction using a
lower level method.Comment: 9 pages, 4 figure
Theoretical study of the insulating oxides and nitrides: SiO2, GeO2, Al2O3, Si3N4, and Ge3N4
An extensive theoretical study is performed for wide bandgap crystalline
oxides and nitrides, namely, SiO_{2}, GeO_{2}, Al_{2}O_{3}, Si_{3}N_{4}, and
Ge_{3}N_{4}. Their important polymorphs are considered which are for SiO_{2}:
-quartz, - and -cristobalite and stishovite, for
GeO_{2}: -quartz, and rutile, for Al_{2}O_{3}: -phase, for
Si_{3}N_{4} and Ge_{3}N_{4}: - and -phases. This work
constitutes a comprehensive account of both electronic structure and the
elastic properties of these important insulating oxides and nitrides obtained
with high accuracy based on density functional theory within the local density
approximation. Two different norm-conserving \textit{ab initio}
pseudopotentials have been tested which agree in all respects with the only
exception arising for the elastic properties of rutile GeO_{2}. The agreement
with experimental values, when available, are seen to be highly satisfactory.
The uniformity and the well convergence of this approach enables an unbiased
assessment of important physical parameters within each material and among
different insulating oxide and nitrides. The computed static electric
susceptibilities are observed to display a strong correlation with their mass
densities. There is a marked discrepancy between the considered oxides and
nitrides with the latter having sudden increase of density of states away from
the respective band edges. This is expected to give rise to excessive carrier
scattering which can practically preclude bulk impact ionization process in
Si_{3}N_{4} and Ge_{3}N_{4}.Comment: Published version, 10 pages, 8 figure
Gamification and Simulation
Gamification and simulation methods are two of the most important components of serious games. In order to create an effective training tool, it is imperative to understand these methods and their relationship to each other. If designed correctly, gamification techniques can build upon simulations to provide an effective training medium, which enhances learning, engagement and motivation in users. This chapter discusses their uses, strengths and weaknesses whilst identifying how to most effectively utilise them in developing serious games
A Common Origin for Neutrino Anarchy and Charged Hierarchies
The generation of exponential flavor hierarchies from extra-dimensional
wavefunction overlaps is re-examined. We find, surprisingly, that coexistence
of anarchic fermion mass matrices with such hierarchies is intrinsic and
natural to this setting. The salient features of charged fermion and neutrino
masses and mixings can thereby be captured within a single framework. Both
Dirac and Majorana neutrinos can be realized. The minimal phenomenological
consequences are discussed, including the need for a fundamental scale far
above the weak scale to adequately suppress flavor-changing neutral currents.
Two broad scenarios for stabilizing this electroweak hierarchy are studied,
warped compactification and supersymmetry. In warped compactifications and
"Flavorful Supersymmetry," where non-trivial flavor structure appears in the
new TeV physics, Dirac neutrinos are strongly favored over Majorana by lepton
flavor violation tests. We argue that this is part of a more general result for
flavor-sensitive TeV-scale physics. Our scenario strongly suggests that the
supersymmetric flavor problem is not solved locally in the extra dimension, but
rather at or below the compactification scale. In the supersymmetric Dirac
case, we discuss how the appearance of light right-handed sneutrinos
considerably alters the physics of dark matter.Comment: Comparison with the Froggatt-Nielsen mechanism omitted. Some
clarifications added. This is the version accepted by PRL with a longer
abstract
Quantum Computing Without Wavefunctions: Time-Dependent Density Functional Theory for Universal Quantum Computation
We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms
Uniform electron gases
We show that the traditional concept of the uniform electron gas (UEG) --- a
homogeneous system of finite density, consisting of an infinite number of
electrons in an infinite volume --- is inadequate to model the UEGs that arise
in finite systems. We argue that, in general, a UEG is characterized by at
least two parameters, \textit{viz.} the usual one-electron density parameter
and a new two-electron parameter . We outline a systematic
strategy to determine a new density functional across the
spectrum of possible and values.Comment: 8 pages, 2 figures, 5 table
Low Temperature Shear Modulus Changes in Solid 4-He and Connection to Supersolidity
Superfluidity, liquid flow without friction, is familiar in helium. The first
evidence for "supersolidity", its analogue in quantum solids, came from recent
torsional oscillator (TO) measurements involving 4-He. At temperatures below
200 mK, TO frequencies increased, suggesting that some of the solid decoupled
from the oscillator. This behavior has been replicated by several groups but
solid 4-He does not respond to pressure differences and persistent currents and
other signatures of superflow have not been seen. Both experiments and theory
indicate that defects are involved. These should also affect the solid's
mechanical behavior and so we have measured the shear modulus of solid 4-He at
low frequencies and strains. We observe large increases below 200 mK, with the
same dependence on measurement amplitude, 3-He impurity concentration and
annealing as the decoupling seen in TO experiments. This unusual elastic
behavior is explained in terms of a dislocation network which is pinned by 3-He
at the lowest temperatures but becomes mobile above 100 mK. The frequency
changes in TO experiments appear to be related to the motion of these
dislocations, perhaps by disrupting a possible supersolid state.Comment: 18 pages, 4 figues, Supplementary Informatio
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