Thermal and quantum fluctuations in chains of ultracold polar molecules

Ultracold polar molecules, in highly anisotropic traps and interacting via a repulsive dipolar potential, may form one-dimensional chains at high densities. According to classical theory, at low temperatures there exists a critical value of the density at which a second-order phase transition from a linear to a zigzag chain occurs. We study the effect of thermal and quantum fluctuations on these self-organized structures using classical and quantum Monte Carlo methods, by means of which we evaluate the pair correlation function and the static structure factor. Depending on the parameters, these functions exhibit properties typical of a crystalline or of a liquid system. We compare the thermal and the quantum results, identifying analogies and differences. Finally, we discuss experimental parameter regimes where the effects of quantum fluctuations on the linear-zigzag transition can be observed.

Ground state of low-dimensional dipolar gases: Linear and zigzag chains

We study the ground-state phase diagram of ultracold dipolar gases in highly anisotropic traps. Starting from a one-dimensional geometry, by ramping down the transverse confinement along one direction, the gas reaches various planar distributions of dipoles. At large linear densities, when the dipolar gas exhibits a crystal-like phase, critical values of the transverse frequency exist below which the configuration exhibits transverse patterns. These critical values are found by means of a classical theory, and are in full agreement with classical Monte Carlo simulations. The study of the quantum system is performed numerically with Monte Carlo techniques and shows that the quantum fluctuations smoothen the transition and make it completely disappear in a gas phase. These predictions could be experimentally tested and would allow one to reveal the effect of zero-point motion on self-organized mesoscopic structures of matter waves, such as the transverse pattern of the zigzag chain.

Path-integral study of a two-dimensional Lennard-Jones glass

The glass transition in a quantum Lennard-Jones mixture is investigated by constant-volume path-integral simulations. Particles are assumed to be distinguishable, and the strength of quantum effects is varied by changing h from zero (the classical case) to one (corresponding to a highly quantum-mechanical regime). Quantum delocalization and zero point energy drastically reduce the sensitivity of structural and thermodynamic properties to the glass transition. Nevertheless, the glass transition temperature T-g can be determined by analyzing the phase space mobility of path-integral centroids. At constant volume, the T-g of the simulated model increases monotonically with increasing h. Low temperature tunneling centers are identified, and the quantum versus thermal character of each center is analyzed. The relation between these centers and soft quasilocalized harmonic vibrations is investigated. Periodic minimizations of the potential energy with respect to the positions of the particles are performed to determine the inherent structure of classical and quantum glassy samples. The geometries corresponding to these energy minima are found to be qualitatively similar in all cases. Systematic comparisons for ordered and disordered structures, harmonic and anharmonic dynamics, classical and quantum systems show that disorder, anharmonicity, and quantum effects are closely interlinked.

Power dissipation in nanoscale conductors: classical, semi-classical and quantum dynamics

Modelling Joule heating is a difficult problem because of the need to introduce correct correlations between the motions of the ions and the electrons. In this paper we analyse three different models of current induced heating (a purely classical model, a fully quantum model and a hybrid model in which the electrons are treated quantum mechanically and the atoms are treated classically). We find that all three models allow for both heating and cooling processes in the presence of a current, and furthermore the purely classical and purely quantum models show remarkable agreement in the limit of high biases. However, the hybrid model in the Ehrenfest approximation tends to suppress heating. Analysis of the equations of motion reveals that this is a consequence of two things: the electrons are being treated as a continuous fluid and the atoms cannot undergo quantum fluctuations. A means for correcting this is suggested.

Effect of quantization of vibrations on the structural properties of crystals

We study the structural effects produced by the quantization of vibrational degrees of freedom in periodic crystals at zero temperature. To this end we introduce a methodology based on mapping a suitable subspace of the vibrational manifold and solving the Schrödinger equation in it. A number of increasingly accurate approximations ranging from the quasiharmonic approximation (QHA) to the vibrational self-consistent field (VSCF) method and the exact solution are described. A thorough analysis of the approximations is presented for model monatomic and hydrogen-bonded chains, and results are presented for a linear H-F chain where the potential-energy surface is obtained via first-principles electronic structure calculations. We focus on quantum nuclear effects on the lattice constant and show that the VSCF is an excellent approximation, meaning that correlation between modes is not extremely important. The QHA is excellent for covalently bonded mildly anharmonic systems, but it fails for hydrogen-bonded ones. In the latter, the zero-point energy exhibits a nonanalytic behavior at the lattice constant where the H atoms center, which leads to a spurious secondary minimum in the quantum-corrected energy curve. An inexpensive anharmonic approximation of noninteracting modes appears to produce rather good results for hydrogen-bonded chains for small system sizes. However, it converges to the incorrect QHA results for increasing size. Isotope effects are studied for the first-principles H-F chain. We show how the lattice constant and the H-F distance increase with decreasing mass and how the QHA proves to be insufficient to reproduce this behavior.

Local temperature in quantum thermal states

We consider blocks of quantum spins in a chain at thermal equilibrium, focusing on their properties from a thermodynamical perspective. In a classical system the temperature behaves as an intensive magnitude, above a certain block size, regardless of the actual value of the temperature itself. However, a deviation from this behavior is expected in quantum systems. In particular, we see that under some conditions the description of the blocks as thermal states with the same global temperature as the whole chain fails. We analyze this issue by employing the quantum fidelity as a figure of merit, singling out in detail the departure from the classical behavior. As it may be expected, we see that quantum features are more prominent at low temperatures and are affected by the presence of zero-temperature quantum phase transitions. Interestingly, we show that the blocks can be considered indeed as thermal states with a high fidelity, provided an effective local temperature is properly identified. Such a result may originate from typical properties of reduced subsystems of energy-constrained Hilbert spaces. Finally, the relation between local and global temperatures is analyzed as a function of the size of the blocks and the system parameters.

Criticality, factorization, and long-range correlations in the anisotropic XY model

We study the long-range quantum correlations in the anisotropic XY model. By first examining the thermodynamic limit, we show that employing the quantum discord as a figure of merit allows one to capture the main features of the model at zero temperature. Furthermore, by considering suitably large site separations we find that these correlations obey a simple scaling behavior for finite temperatures, allowing for efficient estimation of the critical point. We also address ground-state factorization of this model by explicitly considering finite-size systems, showing its relation to the energy spectrum and explaining the persistence of the phenomenon at finite temperatures. Finally, we compute the fidelity between finite and infinite systems in order to show that remarkably small system sizes can closely approximate the thermodynamic limit.

Optimization through quantum annealing: theory and some applications

Quantum annealing is a promising tool for solving optimization problems, similar in some ways to the traditional ( classical) simulated annealing of Kirkpatrick et al. Simulated annealing takes advantage of thermal fluctuations in order to explore the optimization landscape of the problem at hand, whereas quantum annealing employs quantum fluctuations. Intriguingly, quantum annealing has been proved to be more effective than its classical counterpart in many applications. We illustrate the theory and the practical implementation of both classical and quantum annealing - highlighting the crucial differences between these two methods - by means of results recently obtained in experiments, in simple toy-models, and more challenging combinatorial optimization problems ( namely, Random Ising model and Travelling Salesman Problem). The techniques used to implement quantum and classical annealing are either deterministic evolutions, for the simplest models, or Monte Carlo approaches, for harder optimization tasks. We discuss the pro and cons of these approaches and their possible connections to the landscape of the problem addressed.

Non-Gaussian distribution of collective operators in quantum spin chains

We numerically analyse the behavior of the full distribution of collective observables in quantum spin chains. While most of previous studies of quantum critical phenomena are limited to the first moments, here we demonstrate how quantum fluctuations at criticality lead to highly non-Gaussian distributions. Interestingly, we show that the distributions for different system sizes collapse on thesame curve after scaling for a wide range of transitions: first and second order quantum transitions and transitions of the Berezinskii–Kosterlitz–Thouless type. We propose and analyse the feasibility of an experimental reconstruction of the distribution using light–matter interfaces for atoms in optical lattices or in optical resonators.

Analytically continued generalized continuum distorted waves

The continuum distorted-wave eikonal-initial-state (CDW-EIS) theory of Crothers and McCann (Crothers DSF and McCann JF, 1983 J. Phys. B: At. Mol. Opt. Phys. 16 3229 ) used to describe ionization in ion-atom collisions is generalized (G) to GCDW-EIS, to incorporate the azimuthal ange dependence into the final-state wavefunction. This is accomplished by the analytic continuation of hydrogenic-like wavefunctions from below to above threshold, using parabolic coordinates and quantum numbers including magnetic quantum numbers, thus providing a more complete set of states. At impact energies lower than 25 ke V u^{-1}, the total CDW-EIS ionization cross section falls off, with decreasing energy, too quickly in comparison with experimental data by Crothers and McCann. The idea behind and motivation for the GCDW-EIS model is to improve the theory with respect to experiment, by including contributions from non-zero magnetic quantum numbers. We also therefore incidentally provide a new derivation of the theory of continuum distorted waves for zero magnetic quantum numbers while simultaneously generalizing it.

Magnetically quantized continuum distorted-wave theory in atomic and molecular collisions

The continuum distorted-wave eikonal initial-state (CDW-EIS) theory of Crothers and McCann (J Phys B 1983, 16, 3229) used to describe ionization in ion-atom collisions is generalized (G) to GCDW-EIS to incorporate the azimuthal angle dependence of each CDW in the final-state wave function. This is accomplished by the analytic continuation of hydrogenic-like wave functions from below to above threshold, using parabolic coordinates and quantum numbers including magnetic quantum numbers, thus providing a more complete set of states. At impact energies lower than 25 keVu(-1), the total ionization cross-section falls off, with decreasing energy, too quickly in comparison with experimental data. The idea behind and motivation for the GCDW-EIS model is to improve the theory with respect to experiment by including contributions from nonzero magnetic quantum numbers. We also therefore incidentally provide a new derivation of the theory of continuum distorted waves for zero magnetic quantum numbers while simultaneously generalizing it. (C) 2004 Wiley Periodicals, Inc.

An understanding of chemoselective hydrogenation on crotonaldehyde over Pt(111) in the free energy landscape: The microkinetics study based on first-principles calculations

Microkinetic model is developed in the free energy landscape based on density functional theory (DFT) to quantitatively investigate the reaction mechanism of chemoselective partial hydrogenation of crotonaldehyde to crotyl alcohol over Pt(1 1 1) at the temperature of 353 K. Three different methods (mobile, immobile and collision theory models) were carried out to obtain free energy barrier of adsorption/desorption processes. The results from mobile and collision theory models are similar. The calculated TOFs from both models are close to the experiment value. However, for the immobile model, in which the free energy barrier of desorption approaches the energy barrier, the calculated TOF is 2 orders of magnitude lower than the other models. The difficulty of adsorption/ desorption may be overestimated in the immobile model. In addition, detailed analyses show that for the surface hydrogenation elementary steps, the entropy and internal energy effects are small under the reaction condition, while the zero-point-energy (ZPE) correction is significant, especially for the multi-step hydrogenation reaction. The total energy with the ZPE correction approaches to the full free energy calculation for the surface reaction under the reaction condition. (c) 2011 Elsevier B.V. All rights reserved.

Photon Production from the Vacuum Close to the Superradiant Transition: Linking the Dynamical Casimir Effect to the Kibble-Zurek Mechanism

The dynamical Casimir effect (DCE) predicts the generation of photons from the vacuum due to the parametric amplification of the quantum fluctuations of an electromagnetic field. The verification of such an effect is still elusive in optical systems due to the very demanding requirements of its experimental implementation. We show that an ensemble of two-level atoms collectively coupled to the electromagnetic field of a cavity, driven at low frequencies and close to a quantum phase transition, stimulates the production of photons from the vacuum. This paves the way to an effective simulation of the DCE through a mechanism that has recently found experimental demonstration. The spectral properties of the emitted radiation reflect the critical nature of the system and allow us to link the detection of the DCE to the Kibble-Zurek mechanism for the production of defects when crossing a continuous phase transition.

Robust nonadiabatic molecular dynamics for metals and insulators

We present a new formulation of the correlated electron-ion dynamics (CEID) scheme, which systematically improves Ehrenfest dynamics by including quantum fluctuations around the mean-field atomic trajectories. We show that the method can simulate models of nonadiabatic electronic transitions and test it against exact integration of the time-dependent Schrodinger equation. Unlike previous formulations of CEID, the accuracy of this scheme depends on a single tunable parameter which sets the level of atomic fluctuations included. The convergence to the exact dynamics by increasing the tunable parameter is demonstrated for a model two level system. This algorithm provides a smooth description of the nonadiabatic electronic transitions which satisfies the kinematic constraints (energy and momentum conservation) and preserves quantum coherence. The applicability of this algorithm to more complex atomic systems is discussed.