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

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

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 $Z_1^3$ correction to the stopping power of a 2DEG for charged particles moving at a fixed distance from the plane of the 2D sheet, $Z_1$ 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 $Z_1^3$ 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.

Statistics and Nos\'e formalism for Ehrenfest dynamics

Quantum dynamics (i.e., the Schr\"odinger equation) and classical dynamics (i.e., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this paper we first show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. Once we know the canonical distribution of a Ehrenfest system, it is straightforward to extend the formalism of Nos\'e (invented to do constant temperature Molecular Dynamics by a non-stochastic method) to our Ehrenfest formalism. This work also provides the basis for extending stochastic methods to Ehrenfest dynamics.Comment: 28 pages, 1 figure. Published version. arXiv admin note: substantial text overlap with arXiv:1010.149

Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Ref. 1. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space $D$, and on the number of classical trajectories $N$ of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.Comment: Revtex 4-1, 14 pages, 2 figures. Final published versio

Lifetimes of image-potential states on copper surfaces

The lifetime of image states, which represent a key quantity to probe the coupling of surface electronic states with the solid substrate, have been recently determined for quantum numbers $n\le 6$ on Cu(100) by using time-resolved two-photon photoemission in combination with the coherent excitation of several states (U. H\"ofer et al, Science 277, 1480 (1997)). We here report theoretical investigations of the lifetime of image states on copper surfaces. We evaluate the lifetimes from the knowledge of the self-energy of the excited quasiparticle, which we compute within the GW approximation of many-body theory. Single-particle wave functions are obtained by solving the Schr\"odinger equation with a realistic one-dimensional model potential, and the screened interaction is evaluated in the random-phase approximation (RPA). Our results are in good agreement with the experimentally determined decay times.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let

Nonlinear energy-loss straggling of protons and antiprotons in an electron gas

The electronic energy-loss straggling of protons and antiprotons moving at arbitrary nonrelativistic velocities in a homogeneous electron gas are evaluated within a quadratic response theory and the random-phase approximation (RPA). These results show that at low and intermediate velocities quadratic corrections reduce significantly the energy-loss straggling of antiprotons, these corrections being, at low-velocities, more important than in the evaluation of the stopping power.Comment: 4 pages, 3 figures, to appear in Phys. Rev.

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