Coherent Raman spectroscopy: From statics to dynamics and kinetics,progress in nonlinear methods

In spite of its 60-year history Raman spectroscopy is still progressing nowadays. Highly stable lasers and short pulse oscillators, perfect electronic data acquisition systems, new nonlinear optical approaches created new exciting perspectives for Raman spectroscopy. One of the most important tendencies is Raman spectroscopy application for studying nonequilibrium states, fast dynamics and kinetics of atoms, molecules and condensed matter. All these problems were until recently regarded as inaccessible for optical spectroscopy. Nonlinear optical techniques of Coherent Anti-Stokes Raman Scattering (CARS) and modulation spectroscopy appeared to be most effective and provided important real-time information on molecular excitation and dissociation dynamics, deep cooling of molecules in a supersonic jet, short laser pulse induced phase transitions at semiconductor interface and so on. Problems yet to be solved include direct measurement of intramolecular vibrational relaxation, conformations in biomolecules, optical “oscilloscopy” of molecular vibrations.     

Construct order parameters from the reduced density matrix spectra

In this paper, we try to establish a connection between a quantum information concept, i.e., the mutual information, and the conventional order parameter in condensed matter physics. We show that non-vanishing mutual information between two subsystems separated by a long distance means the existence of long-range orders in the system. By analyzing the spectra of the reduced density matrices that are used to calculate the mutual information, we show how to derive the local order operators that identify various ordered phases in condensed matter physics.     

Topical issue on Geometry, Integrability and Nonlinearity in Condensed Matter Physics

Recent developments in the study of nonlinear phenomena have led to the realization that a combination of the concepts of integrability, geometry and topology provides a new powerful framework for describing a great variety of physical systems. It was therefore felt that the compilation of a special issue comprising articles on the interdiseiplinary topic of Geometry, Integrability and Nonlinearity in Condensed Matter Physics, would indeed be timely. The enthusiastic response and support that we received from the active researchers in this subject, when we organized an International Conference on the above topic from July 15 to July 20, 2001, in Bansko, Bulgaria, provided a further motivation for undertaking this task. As the topic is interdisciplinary in nature, the articles in this volume contain new results on a wide range of subjects. These include among others, integrable equations and the interplay between geometry and nonlinearity, the role of optical solitons in communication. (and, possibly, computation), common nonlinear and geometrical aspects of condensed matter, field theory, and so on. The increasingly important role played by geometry and topology in diverse areas such as the quantum Hall effect, localization, deformation and elasticity, quasiparticle kinetics and dynamics, spin systems, membranes, is highlighted in some of the articles. There are papers in which essential links of nonlinearity to differential geometry are identified and many elegant mathematical methods are presented. Some other articles focus on how the mathematical tools of geometry and nonlinear analysis can be applied to solve certain physical problems. Given the vast range of titles, it was difficult to strictly divide the contributions into distinct categories. Except for the pedagogical introductory article by Rajaraman titled "CP _N Solitons in Quantum Hall Systems", which essentially "sets the stage" for the various themes covered, we have grouped the articles broadly under the following headings: Geometry, integrability and mathematical physics; Solitons: Interaction phenomena, nonlinear optics; Condensed matter physics; Soft condensed matter physics; Quantum phenomena. We gratefully acknowledge the support from Los Alamos National Lab, USA; Université de Cergy-Pontoise, France; The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy and the Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria, in putting this special volume together. We believe that the cross-fertilization and synergy of a host of ideas in seemingly disparate fields of physics would lead to the natural emergence of new paradigms, which in turn could pave the way for collaborative research to arrive at new solutions of complex nonlinear problems. It is our hope that this topical issue will be useful in providing an impetus for achieving this broad objective. Radha Balakrishnan, Chennai, India Rossen Dandoloff, Cergy-Pontoise, France Vladimir Gerdjikov, Sofia, Bulgaria Dimitar Pushkarov, Sofia, Bulgaria Avadh Saxena, Los Alamos, USA     

Robust outer synchronization between two complex networks with fractional order dynamics

Synchronization between two coupled complex networks with fractional-order dynamics, hereafter referred to as outer synchronization, is investigated in this work. In particular, we consider two systems consisting of interconnected nodes. The state variables of each node evolve with time according to a set of (possibly nonlinear and chaotic) fractional-order differential equations. One of the networks plays the role of a master system and drives the second network by way of an open-plus-closed-loop (OPCL) scheme. Starting from a simple analysis of the synchronization error and a basic lemma on the eigenvalues of matrices resulting from Kronecker products, we establish various sets of conditions for outer synchronization, i.e., for ensuring that the errors between the state variables of the master and response systems can asymptotically vanish with time. Then, we address the problem of robust outer synchronization, i.e., how to guarantee that the states of the nodes converge to common values when the parameters of the master and response networks are not identical, but present some perturbations. Assuming that these perturbations are bounded, we also find conditions for outer synchronization, this time given in terms of sets of linear matrix inequalities (LMIs). Most of the analytical results in this paper are valid both for fractional-order and integer-order dynamics. The assumptions on the inner (coupling) structure of the networks are mild, involving, at most, symmetry and diffusivity. The analytical results are complemented with numerical examples. In particular, we show examples of generalized and robust outer synchronization for networks whose nodes are governed by fractional-order Lorenz dynamics.     

Attosecond physics with neutrons and electrons: Ultrafast entanglement and decoherence phenomena involving protons in condensed matter and molecules

Nuclei and electrons in condensed matter and/or molecules are usually entangled, due to the prevailing electromagnetic interactions. Usually, the “environment” of a microscopic scattering system (e.g., a proton) causes an ultrafast decoherence, thus making atomic and/or nuclear entanglement effects not directly accessible to experiments. However, neutron Compton scattering (NCS) and electron Compton scattering represent ultrafast techniques operating in the sub-femtosecond timescale, thus opening a way for investigation of such dehoherence and short-lived entanglement phenomena of atoms in molecules and condensed matter. The experimental context of NCS and a new striking scattering effect from protons (H-atoms) in several condensed systems and molecules are described. In short, one observes an “anomalous” decrease of scattering intensity from protons, which seem to become partially “invisible” to the neutrons. The experiments apply large energy (several electronvolts) and momentum (10–200 Å^?1 transfers, and the collisional (or scattering) time between the neutron and a struck proton is only 100–1000 attoseconds long. Similar results are also obtained with electron-atom Compton scattering at large momentum transfers. As an example, we present new NCS experimental results from a single crystal, which also provide new physical insights into the attosecond quantum dynamics of protons in molecules and condensed matter. Theoretical discussions and models are presented which show that the effect under consideration is caused by the non-unitary time evolution (due to decoherence) of open quantum systems during the ultrashort, but finite, time-window of the neutron-proton scattering process. The conceptual connection with the well known Quantum Zeno Effect is pointed out. The experimental results, together with their qualitative interpretation “from first principles,” show that epithermal neutrons being available at spallation sources, and electron spectrometers providing large momentum transfers, may represent novel tools for investigation of thus far unknown physical and chemical attosecond phenomena.     

Glassy behavior of light

We study the nonlinear dynamics of a multimode random laser using the methods of statistical physics of disordered systems. A replica-symmetry breaking phase transition is predicted as a function of the pump intensity. We thus show that light propagating in a random nonlinear medium displays glassy behavior; i.e., the photon gas has a multitude of metastable states and a nonvanishing complexity, corresponding to mode-locking processes in random lasers. The present work reveals the existence of new physical phenomena, and demonstrates how nonlinear optics and random lasers can be a benchmark for the modern theory of complex systems and glasses.     

Hetero-Bäcklund transformation and similarity reduction of an extended (2+1)-dimensional coupled Burgers system in fluid mechanics

Nowadays, the Burgers-type equations are seen in plasma astrophysics, ocean dynamics, atmospheric science, computational fluid mechanics, cosmology, condensed matter physics, statistical physics, nonlinear acoustics, vehicular traffic, electronic transport, and so forth. In this Letter, we investigate an extended (2+1)-dimensional coupled Burgers system in fluid mechanics. With symbolic computation and with reference to the velocity components in fluid-related problems, we construct a hetero-Bäcklund transformation and a similarity reduction, depending on the coefficients in the system.     

Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in “artificial” magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed.

Motto:     

Reconstruction of dynamic structures of experimental setups based on measurable experimental data only

Nowadays, massive amounts of data have been accumulated in various and wide fields, it has become today one of the central issues in interdisciplinary fields to analyze existing data and extract as much useful information as possible from data. It is often that the output data of systems are measurable while dynamic structures producing these data are hidden,and thus studies to reveal system structures by analyzing available data, i.e., reconstructions of systems become one of the most important tasks of information extractions. In the past, most of the works in this respect were based on theoretical analyses and numerical verifications. Direct analyses of experimental data are very rare. In physical science, most of the analyses of experimental setups were based on the first principles of physics laws, i.e., so-called top-down analyses. In this paper, we conducted an experiment of "Boer resonant instrument for forced vibration"(BRIFV) and inferred the dynamic structure of the experimental set purely from the analysis of the measurable experimental data, i.e., by applying the bottomup strategy. Dynamics of the experimental set is strongly nonlinear and chaotic, and it's subjects to inevitable noises. We proposed to use high-order correlation computations to treat nonlinear dynamics; use two-time correlations to treat noise effects. By applying these approaches, we have successfully reconstructed the structure of the experimental setup, and the dynamic system reconstructed with the measured data reproduces good experimental results in a wide range of parameters.     

Dynamics of Hubbard Nano‐Clusters Following Strong Excitation

The Hubbard model is a prototype for strongly correlated electrons in condensed matter, for molecules and fermions or bosons in optical lattices. While the equilibrium properties of these systems have been studied in detail, the excitation and relaxation dynamics following a perturbation of the system are only poorly explored. Here, we present results for the dynamics of electrons following nonlinear strong excitation that are based on a nonequilibrium Green functions approach. We focus on small systems—“Hubbard nano‐clusters”—that contain just a few particles where, in addition to the correlation effects, finite size effects and spatial inhomegeneity can be studied systematically. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Communicating with optical hyperchaos: information encryption and decryption in delayed nonlinear feedback systems

Recent theoretical studies and experimental demonstrations have shown the possibility of using chaos for the encryption of message signals in communication systems. Chaos is generated by systems with delayed nonlinear feedback, which feature hyperchaotic (i.e., of high dimensionality) dynamics. The different ways for the injection of the information in the emitter and the process of the synchronization of the receiver are considered. The analysis of all the possibilities can be used to choose the correct topology of communication systems and, more generally, to explain the behavior of any chaotic systems ruled by nonlinear difference-differential equations.     

Emergence of the self-similar property in gene expression dynamics

Many theoretical models have recently been proposed to understand the structure of cellular systems composed of various types of elements (e.g., proteins, metabolites and genes) and their interactions. However, the cell is a highly dynamic system with thousands of functional elements fluctuating across temporal states. Therefore, structural analysis alone is not sufficient to reproduce the cell's observed behavior.In this article, we analyze the gene expression dynamics (i.e., how the amount of mRNA molecules in cell fluctuate in time) by using a new constructive approach, which reveals a symmetry embedded in gene expression fluctuations and characterizes the dynamical equation of gene expression (i.e., a specific stochastic differential equation). First, by using experimental data of human and yeast gene expression time series, we found a symmetry in short-time transition probability from time t to time t+1. We call it self-similarity symmetry (i.e., the gene expression short-time fluctuations contain a repeating pattern of smaller and smaller parts that are like the whole, but different in size). Secondly, we reconstruct the global behavior of the observed distribution of gene expression (i.e., scaling-law) and the local behavior of the power-law tail of this distribution. This approach may represent a step forward toward an integrated image of the basic elements of the whole cell.     

活力物质的非平衡结构和动力学

活力物质是一类典型的非平衡态体系,已成为软凝聚态物理新近发展的一个重要研究方向.活力物质由微驱动粒子组成,驱动力独立地施加在体系中的每个粒子上.文章概述了作者平时研究中所关注的一些活力物质系统中出现的十分有意义的现象,着重介绍了活力物质系统的构成,以及活力物质的气液态、铁磁态、向列相态和凝胶状态中涌现出的非平衡结构及其特殊的动力学行为.     

Superdiffusion and encounter rates in diluted,low dimensional worlds

Rate limitation due to encounters is fundamental to many ecological interactions. Since encounter rate governs reaction rates, and thus, dynamics of systems, it deserves systematic study. In classical population biology, ecological dynamics rely on the assumption of perfectly mixed interacting entities (e.g., individuals, populations, etc.) in a spaceless world. The so-called mean field assumption assumes that encounter rates are driven exclusively by changes in the density of the interacting entities and not on how they are distributed or move in space. Therefore, the mean field assumption does not give any insight into relevant spatiotemporal statistical properties produced by the trajectories of moving entities through space. In the present study, we develop spatially explicit simulations of random walking particles (i.e., Lévy walkers) to evaluate encounter rate constraints beyond the mean field assumption. We show that encounter rate fluctuations are driven not only by physical aspects such as the size or the velocity of the interacting particles, but also by different motion patterns. In particular, superdiffusion phenomena might be relevant at low densities and/or low spatial dimensionality. Finally, we discuss potential adaptive responses of living organisms that may allow individuals to control how they diffuse through space and/or the spatial dimensions employed in the exploration process.     

Squeezed thermal spin states of magnons in the ferromagnet

In this paper, we discuss squeezed thermal spin states of magnons that are described by the Heisenberg Hamiltonian in the ferromagnet, in which the magnon system possesses a new kind of quasiparticle, which we call ferromagnon, i.e. a “dressed” quasi-particle obtained from the magnons by a Bogoliubov-Valatin transformation . Generally, the mass and noise properties of ferromagnons possess potentially important and novel effects in condensed matter physics, which have extensive application in the fields of science and technology. Moreover, it is convenient to introduce the Holstein-Primakoff method, in order to take into account the nonlinear interaction among spin waves. At last we describe the quantum fluctuations of spin-components in the squeezed thermal spin states of magnons and their temperature-dependence. Below some temperature, the squeezed thermal spin states of ferromagnons show squeeze effect.     

Dynamics and transport in mean-field coupled, many degrees-of-freedom, area-preserving nontwist maps

Area-preserving nontwist maps, i.e., maps that violate the twist condition, arise in the study of degenerate Hamiltonian systems for which the standard version of the Kolmogorov-Arnold-Moser (KAM) theorem fails to apply. These maps have found applications in several areas including plasma physics, fluid mechanics, and condensed matter physics. Previous work has limited attention to maps in 2-dimensional phase space. Going beyond these studies, in this paper, we study nontwist maps with many-degrees-of-freedom. We propose a model in which the different degrees of freedom are coupled through a mean-field that evolves self-consistently. Based on the linear stability of period-one and period-two orbits of the coupled maps, we construct coherent states in which the degrees of freedom are synchronized and the mean-field stays nearly fixed. Nontwist systems exhibit global bifurcations in phase space known as separatrix reconnection. Here, we show that the mean-field coupling leads to dynamic, self-consistent reconnection in which transport across invariant curves can take place in the absence of chaos due to changes in the topology of the separatrices. In the context of self-consistent chaotic transport, we study two novel problems: suppression of diffusion and breakup of the shearless curve. For both problems, we construct a macroscopic effective diffusion model with time-dependent diffusivity. Self-consistent transport near criticality is also studied, and it is shown that the threshold for global transport as function of time is a fat-fractal Cantor-type set.     

Nonequilibrium Green Functions Approach to Strongly Correlated Fermions in Lattice Systems

Quantum dynamics in strongly correlated systems are of high current interest in many fields including dense plasmas, nuclear matter and condensed matter and ultracold atoms. An important model case are fermions in lattice systems that is well suited to analyze, in detail, a variety of electronic and magnetic properties of strongly correlated solids. Such systems have recently been reproduced with fermionic atoms in optical lattices which allow for a very accurate experimental analysis of the dynamics and of transport processes such as diffusion. The theoretical analysis of such systems far from equilibrium is very challenging since quantum and spin effects as well as correlations have to be treated non‐perturbatively. The only accurate method that has been successful so far are density matrix renormalization group (DMRG) simulations. However, these simulations are presently limited to one‐dimensional (1D) systems and short times. Extension of quantum dynamics simulations to two and three dimensions is commonly viewed as one of the major challenges in this field. Recently we have reported a breakthrough in this area [N. Schlünzen et al., Phys. Rev. B (2016)] where we were able to simulate the expansion dynamics of strongly correlated fermions in a Hubbard lattice following a quench of the confinement potential in 1D, 2D and 3D. The results not only exhibited excellent agreement with the experimental data but, in addition, revealed new features of the short‐time dynamics where correlations and entanglement are being build up. The method used in this work are nonequilibrium Green functions (NEGF) which are found to be very powerful in the treatment of fermionic lattice systems filling the gap presently left open by DMRG in 2D and 3D. In this paper we present a detailed introduction in the NEGF approach and its application to inhomogeneous Hubbard clusters. In detail we discuss the proper strong coupling approximation which is given by T ‐matrix selfenergies that sum up two‐particle scattering processes to infinite order. The efficient numerical implemen‐tation of the method is discussed in detail as it has allowed us to achieve dramatic performance gains. This has been the basis for the treatment of more than 100 particles over large time intervals. The numerical results presented in this paper concentrate on the diffusion in 1D to 3D lattices. We find that the expansion dynamics consist of three different phases that are linked with the build‐up of correlations. In the long time limit, a universal scaling with the particle number is revealed. By extrapolating the expansion velocities to the macroscopic limit, the obtained results show excellent agreement with recent experiments on ultracold fermions in optical lattices. Moreover we present results for the site‐resolved behavior of correlations and entanglement that can be directly compared with experiments using the recently developed atomic microscope technique. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Torsional monopoles and torqued geometries in gravity and condensed matter

Torsional degrees of freedom play an important role in modern gravity theories as well as in condensed matter systems where they can be modeled by defects in solids. Here we isolate a class of torsion models that support torsion configurations with a localized, conserved charge that adopts integer values. The charge is topological in nature, and the torsional configurations can be thought of as torsional "monopole" solutions. We explore some of the properties of these configurations in gravity models with a nonvanishing curvature and discuss the possible existence of such monopoles in condensed matter systems. To conclude, we show how the monopoles can be thought of as a natural generalization of the Cartan spiral staircase.     

Atomic collapse,Lorentz boosts,Klein scattering,and other quantum-relativistic phenomena in graphene

Electrons in graphene, which behave as massless relativistic Dirac particles, provide a new perspective on the relation between condensed matter and high-energy physics. We discuss atomic collapse, a phenomenon in which discrete energy levels of superheavy atoms are transformed into resonant states. Charge impurities in graphene provide a convenient condensed matter system in which this effect can be explored. Relativistic dynamics also manifests itself in graphene p–n junctions. We show how the transport problem in the presence of a magnetic field can be solved with the help of a Lorentz transformation, and use it to investigate magnetotransport in p–n junctions. Finally, we review a recent proposal to use Fabry–Pérot resonances in p–n–p structures as a vehicle to investigate Klein scattering, another hallmark phenomenon of relativistic dynamics.