593 research outputs found
Nonlinear screening in two-dimensional electron gases
We have performed self-consistent calculations of the nonlinear screening of
a point charge Z in a two-dimensional electron gas using a density functional
theory method. We find that the screened potential for a Z=1 charge supports a
bound state even in the high density limit where one might expect perturbation
theory to apply. To explain this behaviour, we prove a theorem to show that the
results of linear response theory are in fact correct even though bound states
exist.Comment: 4 pages, 4 figure
A Proof of Tarski’s Fixed Point Theorem by Application of Galois Connections
Two examples of Galois connections and their dual forms are considered. One
of them is applied to formulate a criterion when a given subset of a complete lattice forms
a complete lattice. The second, closely related to the first, is used to prove in a short way
the Knaster-Tarski’s fixed point theore
An exact expression to calculate the derivatives of position-dependent observables in molecular simulations with flexible constraints
In this work, we introduce an algorithm to compute the derivatives of
physical observables along the constrained subspace when flexible constraints
are imposed on the system (i.e., constraints in which the hard coordinates are
fixed to configuration-dependent values). The presented scheme is exact, it
does not contain any tunable parameter, and it only requires the calculation
and inversion of a sub-block of the Hessian matrix of second derivatives of the
function through which the constraints are defined. We also present a practical
application to the case in which the sought observables are the Euclidean
coordinates of complex molecular systems, and the function whose minimization
defines the constraints is the potential energy. Finally, and in order to
validate the method, which, as far as we are aware, is the first of its kind in
the literature, we compare it to the natural and straightforward
finite-differences approach in three molecules of biological relevance:
methanol, N-methyl-acetamide and a tri-glycine peptideComment: 13 pages, 8 figures, published versio
Efficient formalism for large scale ab initio molecular dynamics based on time-dependent density functional theory
A new "on the fly" method to perform Born-Oppenheimer ab initio molecular
dynamics (AIMD) is presented. Inspired by Ehrenfest dynamics in time-dependent
density functional theory, the electronic orbitals are evolved by a
Schroedinger-like equation, where the orbital time derivative is multiplied by
a parameter. This parameter controls the time scale of the fictitious
electronic motion and speeds up the calculations with respect to standard
Ehrenfest dynamics. In contrast to other methods, wave function orthogonality
needs not be imposed as it is automatically preserved, which is of paramount
relevance for large scale AIMD simulations.Comment: 5 pages, 3 color figures, revtex4 packag
Abstract Interpretation of Supermodular Games
Supermodular games find significant applications in a variety of models,
especially in operations research and economic applications of noncooperative
game theory, and feature pure strategy Nash equilibria characterized as fixed
points of multivalued functions on complete lattices. Pure strategy Nash
equilibria of supermodular games are here approximated by resorting to the
theory of abstract interpretation, a well established and known framework used
for designing static analyses of programming languages. This is obtained by
extending the theory of abstract interpretation in order to handle
approximations of multivalued functions and by providing some methods for
abstracting supermodular games, in order to obtain approximate Nash equilibria
which are shown to be correct within the abstract interpretation framework
Nonextensive thermodynamic functions in the Schr\"odinger-Gibbs ensemble
Schr\"odinger suggested that thermodynamical functions cannot be based on the
gratuitous allegation that quantum-mechanical levels (typically the orthogonal
eigenstates of the Hamiltonian operator) are the only allowed states for a
quantum system [E. Schr\"odinger, Statistical Thermodynamics (Courier Dover,
Mineola, 1967)]. Different authors have interpreted this statement by
introducing density distributions on the space of quantum pure states with
weights obtained as functions of the expectation value of the Hamiltonian of
the system.
In this work we focus on one of the best known of these distributions, and we
prove that, when considered in composite quantum systems, it defines partition
functions that do not factorize as products of partition functions of the
noninteracting subsystems, even in the thermodynamical regime. This implies
that it is not possible to define extensive thermodynamical magnitudes such as
the free energy, the internal energy or the thermodynamic entropy by using
these models. Therefore, we conclude that this distribution inspired by
Schr\"odinger's idea can not be used to construct an appropriate quantum
equilibrium thermodynamics.Comment: 32 pages, revtex 4.1 preprint style, 5 figures. Published version
with several changes with respect to v2 in text and reference
Quadratic electronic response of a two-dimensional electron gas
The electronic response of a two-dimensional (2D) electron system represents
a key quantity in discussing one-electron properties of electrons in
semiconductor heterojunctions, on the surface of liquid helium and in
copper-oxide planes of high-temperature superconductors. We here report an
evaluation of the wave-vector and frequency dependent dynamical quadratic
density-response function of a 2D electron gas (2DEG), within a self-consistent
field approximation. We use this result to find the correction to the
stopping power of a 2DEG for charged particles moving at a fixed distance from
the plane of the 2D sheet, being the projectile charge. We reproduce, in
the high-density limit, previous full nonlinear calculations of the stopping
power of a 2DEG for slow antiprotons, and we go further to calculate the
correction to the stopping power of a 2DEG for a wide range of
projectile velocities. Our results indicate that linear response calculations
are, for all projectile velocities, less reliable in two dimensions than in
three dimensions.Comment: 17 pages, 5 figures, to appear in Phys. Rev.
Inelastic decay rate of quasiparticles in a two-dimensional spin-orbit coupled electron system
We present a study of the inelastic decay rate of quasiparticles in a
two-dimensional electron gas with spin-orbit interaction. The study is done
within the G0W0 approximation. The spin-orbit interaction is taken in the most
general form that includes both Rashba and Dresselhaus contributions linear in
magnitude of the electron 2D momentum. Spin-orbit interaction effect on the
inelastic decay rate is examined at different parameters characterizing the
interaction strength in the electron gas.Comment: 5 pages, 4 figure
Role of bulk and surface phonons in the decay of metal surface states
We present a comprehensive theoretical investigation of the electron-phonon
contribution to the lifetime broadening of the surface states on Cu(111) and
Ag(111), in comparison with high-resolution photoemission results. The
calculations, including electron and phonon states of the bulk and the surface,
resolve the relative importance of the Rayleigh mode, being dominant for the
lifetime at small hole binding energies. Including the electron-electron
interaction, the theoretical results are in excellent agreement with the
measured binding energy and temperature dependent lifetime broadening.Comment: 4 pages, 3 figure
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