134 research outputs found
Interacting Electrons, Spin Statistics, and Information Theory
We consider a nearly (or quasi) uniform gas of interacting electrons for which spin statistics play a crucial role. A previously developed procedure, based on the extension of the Levy–Lieb constrained search principle and Monte Carlo sampling of electron configurations in space, allows us to approximate the form of the kinetic-energy functional. For a spinless electron gas, this procedure led to a correlation term, which had the form of the Shannon entropy, but the resulting kinetic-energy functional does not satisfy the Lieb–Thirring inequality, which is rigorous and one of the most general relations regarding the kinetic energy. In this paper, we show that when the fermionic character of the electrons is included via a statistical spin approach, our procedure leads to correlation terms, which also have the form of the Shannon entropy and the resulting kinetic-energy functional does satisfy the Lieb–Thirring inequality. In this way we further strengthen the connection between Shannon entropy and electron correlation and, more generally, between information theory and quantum mechanics
Variational approach to dequantization
We present a dequantization procedure based on a variational approach whereby
quantum fluctuations latent in the quantum momentum are suppressed. This is
done by adding generic local deformations to the quantum momentum operator
which give rise to a deformed kinetic term quantifying the amount of
``fuzzyness'' caused by such fluctuations. Considered as a functional of such
deformations, the deformed kinetic term is shown to possess a unique minimum
which is seen to be the classical kinetic energy. Furthermore, we show that
extremization of the associated deformed action functional introduces an
essential nonlinearity to the resulting field equations which are seen to be
the classical Hamilton-Jacobi and continuity equations. Thus, a variational
procedure determines the particular deformation that has the effect of
suppressing the quantum fluctuations, resulting in dequantization of the
system.Comment: 6 pages, 1 figure. v2: changes in presentation and conten
Path Integral Molecular Dynamics within the Grand Canonical-like Adaptive Resolution Technique: Simulation of Liquid Water
Quantum effects due to the spatial delocalization of light atoms are treated
in molecular simulation via the path integral technique. Among several methods,
Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to
investigate properties induced by spatial delocalization of atoms; however
computationally this technique is very demanding. The abovementioned limitation
implies the restriction of PIMD applications to relatively small systems and
short time scales. One possible solution to overcome size and time limitation
is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme
(AdResS). AdResS requires a relatively small region treated at path integral
level and embeds it into a large molecular reservoir consisting of generic
spherical coarse grained molecules. It was previously shown that the
realization of the idea above, at a simple level, produced reasonable results
for toy systems or simple/test systems like liquid parahydrogen. Encouraged by
previous results, in this paper we show the simulation of liquid water at room
conditions where AdResS, in its latest and more accurate Grand-Canonical-like
version (GC-AdResS), is merged with two of the most relevant PIMD techniques
available in literature. The comparison of our results with those reported in
literature and/or with those obtained from full PIMD simulations shows a highly
satisfactory agreement
Is there a third order phase transition for supercritical fluids?
We prove that according to Molecular Dynamics (MD) simulations of liquid
mixtures of Lennard-Jones (L-J) particles, there is no third order phase
transition in the supercritical regime beyond Andrew's critical point. This
result is in open contrast with recent theoretical studies and experiments
which instead suggest not only its existence but also its universality
regarding the chemical nature of the fluid. We argue that our results are solid
enough to go beyond the limitations of MD and the generic character of L-J
models, thus suggesting a rather smooth liquid-vapor thermodynamic behavior of
fluids in supercritical regime.Comment: 13 pages, 6 figure
An analytic expression for the electronic correlation term of the kinetic functional
We propose an analytic formula for the non-local Fisher information
functional, or electronic kinetic correlation term, appearing in the expression
of the kinetic density functional. Such an explicit formula is constructed on
the basis of well-founded physical arguments and a rigorous mathematical
prescription
Adaptive Resolution Molecular Dynamics Simulation: Changing the Degrees of Freedom on the Fly
We present a new adaptive resolution technique for efficient particle-based
multiscale molecular dynamics (MD) simulations. The presented approach is
tailor-made for molecular systems where atomistic resolution is required only
in spatially localized domains whereas a lower mesoscopic level of detail is
sufficient for the rest of the system. Our method allows an on-the-fly
interchange between a given molecule's atomic and coarse-grained level of
description, enabling us to reach large length and time scales while spatially
retaining atomistic details of the system. The new approach is tested on a
model system of a liquid of tetrahedral molecules. The simulation box is
divided into two regions: one containing only atomistically resolved
tetrahedral molecules, the other containing only one particle coarse-grained
spherical molecules. The molecules can freely move between the two regions
while changing their level of resolution accordingly. The coarse-grained and
the atomistically resolved systems have the same statistical properties at the
same physical conditions.Comment: 17 pages, 11 figures, 5 table
On the upper bound of the electronic kinetic energy in terms of density functionals
We propose a simple density functional expression for the upper bound of the
kinetic energy for electronic systems. Such a functional is valid in the limit
of slowly varying density, its validity outside this regime is discussed by
making a comparison with upper bounds obtained in previous work. The advantages
of the functional proposed for applications to realistic systems is briefly
discussed.Comment: 10 pages, no figure
Classical kinetic energy, quantum fluctuation terms and kinetic-energy functionals
We employ a recently formulated dequantization procedure to obtain an exact
expression for the kinetic energy which is applicable to all kinetic-energy
functionals. We express the kinetic energy of an N-electron system as the sum
of an N-electron classical kinetic energy and an N-electron purely quantum
kinetic energy arising from the quantum fluctuations that turn the classical
momentum into the quantum momentum. This leads to an interesting analogy with
Nelson's stochastic approach to quantum mechanics, which we use to conceptually
clarify the physical nature of part of the kinetic-energy functional in terms
of statistical fluctuations and in direct correspondence with Fisher
Information Theory. We show that the N-electron purely quantum kinetic energy
can be written as the sum of the (one-electron) Weizsacker term and an
(N-1)-electron kinetic correlation term. We further show that the Weizsacker
term results from local fluctuations while the kinetic correlation term results
from the nonlocal fluctuations. For one-electron orbitals (where kinetic
correlation is neglected) we obtain an exact (albeit impractical) expression
for the noninteracting kinetic energy as the sum of the classical kinetic
energy and the Weizsacker term. The classical kinetic energy is seen to be
explicitly dependent on the electron phase and this has implications for the
development of accurate orbital-free kinetic-energy functionals. Also, there is
a direct connection between the classical kinetic energy and the angular
momentum and, across a row of the periodic table, the classical kinetic energy
component of the noninteracting kinetic energy generally increases as Z
increases.Comment: 10 pages, 1 figure. To appear in Theor Chem Ac
Interacting electrons, spin statistics, and information theory
We consider a nearly (or quasi) uniform gas of interacting electrons for which spin statistics play a crucial role. A previously developed procedure, based on the extension of the Levy–Lieb constrained search principle and Monte Carlo sampling of electron configurations in space, allows us to approximate the form of the kinetic-energy functional. For a spinless electron gas, this procedure led to a correlation term, which had the form of the Shannon entropy, but the resulting kinetic-energy functional does not satisfy the Lieb–Thirring inequality, which is rigorous and one of the most general relations regarding the kinetic energy. In this paper, we show that when the fermionic character of the electrons is included via a statistical spin approach, our procedure leads to correlation terms, which also have the form of the Shannon entropy and the resulting kinetic-energy functional does satisfy the Lieb–Thirring inequality. In this way we further strengthen the connection between Shannon entropy and electron correlation and, more generally, between information theory and quantum mechanics
Exploring the conformational dynamics of alanine dipeptide in solution subjected to an external electric field: A nonequilibrium molecular dynamics simulation
In this paper, we investigate the conformational dynamics of alanine
dipeptide under an external electric field by nonequilibrium molecular dynamics
simulation. We consider the case of a constant and of an oscillatory field. In
this context we propose a procedure to implement the temperature control, which
removes the irrelevant thermal effects of the field. For the constant field
different time-scales are identified in the conformational, dipole moment, and
orientational dynamics. Moreover, we prove that the solvent structure only
marginally changes when the external field is switched on. In the case of
oscillatory field, the conformational changes are shown to be as strong as in
the previous case, and non-trivial nonequilibrium circular paths in the
conformation space are revealed by calculating the integrated net probability
fluxes.Comment: 23 pages, 12 figure
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