Table of contents

A separable x-y model is solved for a specialized vector potential (no magnetic and weak electric fields) penetrating slowly, adiabatically into and across a rectangular box to which an electron is confined. The time-dependent Schrödinger equation has adiabatic solutions, in which gradual phase acquisitions occur for parts of the electronic wave function. For a closed trajectory of the source, the initial and after-return wave functions are shown to be simultaneously co-degenerate solutions of the Hamiltonian, and this situation repeats itself for further cyclic motion of the source.

The Fractional Langevin Equation (FLE) describes a non-Markovian Generalized Brownian Motion with long time persistence (superdiffusion), or anti-persistence (subdiffusion) of both velocity-velocity correlations, and position increments. It presents a case of the Generalized Langevin Equation (GLE) with a singular power law memory kernel. We propose and numerically realize a numerically efficient and reliable Markovian embedding of this superdiffusive GLE, which accurately approximates the FLE over many, about r=N log₁₀ b−2, time decades, where N denotes the number of exponentials used to approximate the power law kernel, and b>1 is a scaling parameter for the hierarchy of relaxation constants leading to this power law. Besides its relation to the FLE, our approach presents an independent and very flexible route to model anomalous diffusion. Studying such a superdiffusion in tilted washboard potentials, we demonstrate the phenomenon of transient hyperdiffusion which emerges due to transient kinetic heating effects.

This paper proposes a simple setup for introducing an artificial magnetic field for neutral atoms in 2D optical lattices. This setup is based on the phenomenon of photon-assisted tunneling and involves a low-frequency periodic driving of the optical lattice. This low-frequency driving does not affect the electronic structure of the atom and can be easily realized by the same means which are employed to create the lattice. We also address the problem of detecting this effective magnetic field. In particular, we study the center-of-mass wave packet dynamics, which is shown to exhibit certain features of cyclotron dynamics of a classical charged particle.

We study coupled irreversible processes. For linear or linearized kinetics with microreversibility, , the kinetic operator K is symmetric in the entropic inner product. This form of Onsager's reciprocal relations implies that the shift in time, exp(Kt), is also a symmetric operator. This generates the reciprocity relations between the kinetic curves. For example, for the Master equation, if we start the process from the i-th pure state and measure the probability p_j(t) of the j-th state (j≠i), and, similarly, measure p_i(t) for the process, which starts at the j-th pure state, then the ratio of these two probabilities p_j(t)/p_i(t) is constant in time and coincides with the ratio of the equilibrium probabilities. We study similar and more general reciprocal relations between the kinetic curves. The experimental evidence provided as an example is from the reversible water gas shift reaction over iron oxide catalyst. The experimental data are obtained using Temporal Analysis of Products (TAP) pulse-response studies. These offer excellent confirmation within the experimental error.

We prove that it is impossible to built a universal quantum machine that produces reflections about an unknown state. We then point out a connection between this result and the optimality of Grover's search algorithm: if such reflection machines were available, it would be possible to accelerate Grover's search algorithm to exponential speedups.

Motivated by the hope that the thermodynamical framework might be extended to strongly interacting statistical systems —complex systems in particular— a number of generalized entropies has been proposed in the past. So far the understanding of their fundamental origin has remained unclear. Here we address this question from first principles. We start by observing that many statistical systems fulfill a set of three general conditions (Shannon-Khinchin axioms, K1–K3). A fourth condition (separability) holds for non-interacting, uncorrelated or Markovian systems only (Shannon-Khinchin axiom, K4). If all four axioms hold the Shannon theorem provides a unique entropy, , i.e. Boltzmann-Gibbs entropy. Here we ask about the consequences of violating the 4th axiom while assuming the first three to hold. By a simple scaling argument we prove that under these conditions each statistical system is characterized by a unique pair of scaling exponents (c, d) in the large size limit. These exponents define equivalence classes for all interacting and non-interacting systems and parametrize a unique entropy, , where Γ(a,b) is the incomplete Gamma function. It covers all systems respecting K1–K3. A series of known entropies can be classified in terms of these equivalence classes. Corresponding distribution functions are special forms of Lambert- exponentials containing —as special cases— Boltzmann, stretched exponential and Tsallis distributions (power laws) —all widely abundant in Nature. In the derivation we assume , with g some function, however more general entropic forms can be classified along the same lines. This is to our knowledge the first ab initio justification for generalized entropies. We discuss a physical example displaying two sets of scaling exponents depending on the external parameters.

Since the anyonic excitations in the Kitaev toric model are perfectly localized quasiparticles, it is possible to generate dynamically the ground state and the excitations of the model Hamiltonian to simulate the anyonic interferometry. We propose a scheme in circuit QED to simulate the interferometry. The qubit-cavity interaction can be engineered to realize effective state control as well as the controlled dynamics of qubits, which are sufficient to prepare the ground states, create and remove the anyonic excitation, and simulate the anyonic interferometry. The simplicity and high fidelity of the operations used open the very promising possibility of simulating fractional statistics of anyons in a macroscopic material in the near future.

We investigate the effects of anisotropy on the stability and dynamics of vortex cluster states which arise in Bose-Einstein condensates. Sufficiently strong anisotropies are shown to stabilize states with arbitrary numbers of vortices that are highly unstable in the isotropic limit. Conversely, anisotropy can be used to destabilize states which are stable in the isotropic limit. Near the linear limit, we identify the bifurcations of vortex states including their emergence from linear eigenstates, while in the strongly nonlinear limit, a particle-like description of the dynamics of the vortices in the anisotropic trap is developed. Both are in very good agreement with numerical results. Collective modes of stabilized many vortex cluster states are demonstrated.

We present an investigation of the fast decompression of a three-dimensional (3D) Bose-Einstein condensate (BEC) at finite temperature using an engineered trajectory for the harmonic trapping potential. Taking advantage of the scaling invariance properties of the time-dependent Gross-Pitaevskii equation, we exhibit a solution yielding a final state identical to that obtained through a perfectly adiabatic transformation, in a much shorter time. Experimentally, we perform a large trap decompression and displacement within a time comparable to the final radial trapping period. By simultaneously monitoring the BEC and the non-condensed fraction, we demonstrate that our specific trap trajectory is valid both for a quantum interacting many-body system and a classical ensemble of non-interacting particles.

By setting laser beams in two-photon Doppler-free configurations for both cascade and Λ-type subsystems in a four-level inverted-Y system, a four-wave mixing (FWM) process is studied and optimized within the Doppler profile. The two-photon ac-Stark effect in the FWM signal is observed, which can be used to determine the energy level shift of the atom due to dressing fields.

The time evolution of the out-of-equilibrium Mott insulator is investigated numerically through calculations of space-time–resolved density and entropy profiles resulting from the release of a gas of ultracold fermionic atoms from an optical trap. For adiabatic, moderate and sudden switching-off of the trapping potential, the out-of-equilibrium dynamics of the Mott insulator is found to differ profoundly from that of the band insulator and the metallic phase, displaying a self-induced stability that is robust within a wide range of densities, system sizes and interaction strengths. The connection between the entanglement entropy and changes of phase, known for equilibrium situations, is found to extend to the out-of-equilibrium regime. Finally, the relation between the system's long time behavior and the thermalization limit is analyzed.

One-way edge states realized in magneto-optical photonic crystals (MOPCs) is generally believed to be robust to scattering from disorders and even strong perturbations. In this work, we experimentally and theoretically study the influence of obstacles on the transport of forward and backward edge states in two-dimensional MOPCs under a dc magnetic field. We find that the passage of electromagnetic wave around the obstacles mainly takes advantage of the formation of new edge states at the new interfaces formed between the obstacle and bulk MOPC. The forward edge states can be blocked when the new edge state channel is cut off or the coupling with the original edge states to the new edge states is strongly reduced.

The possibility of deep parametric decay instability suppression by launching a complementary (small power) pump wave possessing a slightly shifted frequency is demonstrated experimentally. This suppression is achieved at an additional pump wave frequency shift equal to the frequency separation of ion acoustic eigenmodes excited in plasma as a result of absolute parametric decay instability. The recovery of microwave power absorption at the second pump turn on is shown using measurements of the plasma luminosity and accelerated electron fluxes.

The linear dispersion relation for surface perturbations, as derived by Levine et al., Phys. Rev. B, 75 (2007) 205312, is extended to include a smooth surface energy anisotropy function with a variable anisotropy strength (from weak to strong, such that sharp corners and slightly curved facets occur on the corresponding Wulff shape). Through detailed parametric studies it is shown that a combination of a wetting interaction and strong anisotropy, and even a wetting interaction alone results in complicated linear stability characteristics of strained and unstrained solid films.

We study a system formed by soft colloidal spheres attracting each other via a square-well potential, using extensive Monte Carlo simulations of various nature. The softness is implemented through a reduction of the infinite part of the repulsive potential to a finite one. For sufficiently low values of the penetrability parameter we find the system to be Ruelle stable with square-well–like behavior. For high values of the penetrability the system is thermodynamically unstable and collapses into an isolated blob formed by a few clusters each containing many overlapping particles. For intermediate values of the penetrability the system has a rich phase diagram with a partial lack of thermodynamic consistency.

Quantitative analysis of the roughness scaling behavior, which is critical in understanding the evolution of surface microstructure, is reported for ZnO thin films grown by RF magnetron sputtering. The strong dependence of global and local growth parameters on the applied RF powers can be highlighted as a unique observation, which has not been available from the typical super-rough scaling studies. For example, the global growth exponent increased from 0.53± 0.02 at 75 W to 1.03± 0.01 at 200 W. The observed dominant anisotropic growth of crystallites at high powers is believed to be the main reason for the power-dependent roughening behavior.

First-principles calculations have been performed to obtain the size- and shape-dependent energetics of the unary nanocrystals made of transition metal elements Ni, Cu, Rh, Pd, Ag, Ir, Pt, or Au. The variation of the nanocrystal chemical potential μ with the interatomic distance d has been studied, leading to derivation of an energy-distance (μ-d) relation. A variety of nanocrystal morphologies have been employed to explore general features of this relation. It is found that the curves representing the μ-d relationship for the entire set of nanocrystals could all be represented by a single universal function, regardless of the atomic species or the nanocrystal morphology or magnetic ground-state.

The self-alignment and optical dichroism of Au nanoparticle chains grown by glancing incidence deposition on rippled Al₂O₃ thin films is investigated. Although the nucleation of the nanoparticles is almost isotropic, their growth is strongly anisotropic resulting in a sharp dependence of their optical transmittance on the orientation of the polarization of the incident light. We show that both the frequency and the spectral width of the transverse and longitudinal surface plasmon resonances can be easily tuned by varying the amount of deposited metal. Such nanostructured materials open perspectives for the development of plasmonic devices endowed with tunable optical dichroism both in the visible and the near infrared regimes.

Crystal-liquid interfaces in nickel are investigated by molecular-dynamics computer simulations. Inhomogeneous systems of size L_x×L_y×L_z with L_z=5L_y are prepared where the crystal fcc phase at different orientations coexists with the liquid phase, separated by planar interfaces in the xy-plane. The lateral dimensions are varied, using two different geometries with L_x=L_y and with L_y≫L_x. In the framework of capillary wave theory (CWT), anisotropic interfacial stiffnesses and tensions are determined using different predictions of CWT with respect to the spectrum, finite-size broadening and different geometries. From a parameterization in terms of cubic harmonics up to 8th order, the anisotropic interfacial free energy is obtained.

We have measured the low-temperature electrical resistivity of Ag:Mn mesoscopic spin glasses prepared by ion implantation with a concentration of 700 ppm. As expected, we observe a clear maximum in the resistivity ρ(T) at a temperature in good agreement with theoretical predictions. Moreover, we observe remanence effects at very weak magnetic fields for the resistivity below the freezing temperature T_sg: upon Field Cooling (fc), we observe clear deviations of ρ(T) as compared with the Zero-Field Cooling (zfc); such deviations appear even for very small magnetic fields, typically in the Gauss range. This onset of remanence for very weak magnetic fields is reminiscent of the typical signature on magnetic susceptibility measurements of the spin glass transition for this generic glassy system.

Propagating fronts arising from bistable reaction-diffusion equations are a purely deterministic effect. Stochastic reaction-diffusion processes also show front propagation which coincides with the deterministic effect in the limit of small fluctuations (usually, large populations). However, for larger fluctuations propagation can be affected. We give an example, based on the classic spruce budworm model, where the direction of wave propagation, i.e., the relative stability of two phases, can be reversed by fluctuations.

In this paper, a multi-assets artificial financial market populated by zero-intelligence traders with finite financial resources is presented. The market is characterized by different types of stocks representing firms operating in different sectors of the economy. Zero-intelligence traders follow a random allocation strategy which is constrained by finite resources, past market volatility and allocation universe. Within this framework, stock price processes exhibit volatility clustering, fat-tailed distribution of returns and reversion to the mean. Moreover, the cross-correlations between returns of different stocks are studied using methods of random matrix theory. The probability distribution of eigenvalues of the cross-correlation matrix shows the presence of outliers, similar to those recently observed on real data for business sectors. It is worth noting that business sectors have been recovered in our framework without dividends as only consequence of random restrictions on the allocation universe of zero-intelligence traders. Furthermore, in the presence of dividend-paying stocks and in the case of cash inflow added to the market, the artificial stock market points out the same structural results obtained in the simulation without dividends. These results suggest a significative structural influence on statistical properties of multi-assets stock market.

We argue about the application of methods of statistical mechanics to free economy (Kusmartsev F. V., Phys. Lett. A, 375 (2011) 966) and find that the most general distribution of money or income in a free-market economy has a general Bose-Einstein distribution form. Therewith the market is described by three parameters: temperature, chemical potential and the space dimensionality. Numerical simulations and a detailed analysis of a generic model confirm this finding.

The shot noise of a quantum dot (QD) coupled to the ferromagnetic terminals under the perturbation of microwave fields (MWFs) in the Kondo regime has been derived by employing the nonequilibrium Green's function approach. The photon-assisted shot noise associated with the spin-polarized electron tunneling in the Kondo regime has been derived and calculated to reveal significant results for spintronics. The modification of shot noise induced by the polarization angle and spin-polarized linewidths exhibits clearly. The Fano factor displays the photon-assisted effect more efficiently for the circumstance of smaller linewidths. The shot noise is suppressed and enhanced by the MWFs, and it shows sub-Poissonian and super-Poissonian features.

In this study, the complex-network approaches are employed to investigate the word form networks and the lemma networks extracted from dependency syntactic treebanks of fifteen different languages. The results show that it is possible to classify human languages by means of the main parameters of complex networks. The complex-network approaches can obtain language classifications as precise as achieved by contemporary word order typology. Clustering experiments point to the fact that the difference between the word form networks and the lemma networks can make for a better classification of languages. In short, the dependency syntactic networks can reflect morphological variation degrees and morphological complexity.

We investigate stall force and polymerization kinetics of rigid protofilaments in a microtubule or interacting filaments in bundles under an external load force in the framework of a discrete growth model. We introduce the concecpt of polymerization cycles to describe the stochastic growth kinetics, which allows us to derive an exact expression for the stall force. We find that the stall force is independent of ensemble geometry and load distribution. Furthermore, the stall force is proportional to the number of filaments and increases linearly with the strength of lateral filament interactions. These results are corroborated by simulations, which also show a strong influence of ensemble geometry on growth kinetics below the stall force.

We predict spontaneous nematic order in an ensemble of active force generators with elastic interactions as a minimal model for early nematic alignment of short stress fibers in non-motile, adhered cells. Mean-field theory is formally equivalent to Maier-Saupe theory for a nematic liquid. However, the elastic interactions are long-ranged (and thus depend on cell shape and matrix elasticity) and originate in cell activity. Depending on the density of force generators, we find two regimes of cellular rigidity sensing for which orientational, nematic order of stress fibers depends on matrix rigidity either in a step-like manner or with a maximum at an optimal rigidity.

We examine the impact of a solid sphere into a fine-grained granular bed. Using high-speed X-ray radiography we track both the motion of the sphere and local changes in the bed packing fraction. Varying the initial packing density as well as the ambient gas pressure, we find a complete reversal in the effect of interstitial gas on the impact response of the bed: The dynamic coupling between gas and grains allows for easier penetration in initially loose beds but impedes penetration in more densely packed beds. High-speed imaging of the local packing density shows that these seemingly incongruous effects have a common origin in the resistance to bed packing changes caused by interstitial air.

An effective "minimum force" hypothesis is proposed for the evolution of aeolian bedforms. The upper limit of the height-spacing ratio suitable for ripples, small-scale dunes and giant dunes is obtained from fluid dynamics by using this hypothesis.

Using the corrected entropy-area relation motivated by the loop quantum gravity, we investigate the validity of the generalized second law of thermodynamics in the framework of modified FRW cosmology. We consider a non-flat universe filled with an interacting viscous dark energy with dark matter and radiation. The boundary of the universe is assumed to be the dynamical apparent horizon. We find out that the generalized second law is always satisfied throughout the history of the universe for any spatial curvature regardless of the dark-energy model.