Investigation of the higher-order exchange interactions in magnetic spin systems has received during last decades increasing attention. In fact, many experimental studies have recently reported physical phenomena that cannot be explained using the standard approach based on theoretical models with pair interactions only. For this reason a lot of effort has been directed to the development theoretical models that may account for higher-order interaction energy terms. In this work we extensively review recent development in this interesting research field with the special emphasis on the works dealing with magnetic systems with higher-order spin interactions. A special attention is payed to the classification of the four-spin interactions that play an important role in magnetic spin systems. The substantial part of this contribution deals with the review of recent theoretical results obtained for various exactly solvable mixed-spin Ising models on decorated lattices. The particular attention is directed to understanding the influence of a special kind of higher-order interaction which is usually called as a three-site four-spin interaction. This interaction among other interesting physical effects also reveals a possible link between higher-order spin interactions and magneto-elastic properties of various real magnetic compound.
We provide an introduction to the theory of quantum measurements that is centered on the pivotal role played by John von Neumann's model. This introduction is accessible to students and researchers from outside the field of foundations of quantum mechanics and presented within a historical context. We first explain the origins and the meaning of the measurement problem in quantum theory, and why it is not present in classical physics. We perform a chronological review of the quantization of action and explain how this led to successive restrictions on what could be measured in atomic phenomena, until the consolidation of the orthodox interpretation of quantum mechanics. The clear separation between quantum system and classical apparatus that causes these restrictions is subverted in von Neumann's paradigmatic model of quantum measurements, a subject whose concepts we explain, while also providing the mathematical tools necessary to apply it to new problems. We show how this model was important in discussing the interpretations of quantum mechanics and how it is still relevant in modern applications. In particular, we explain in detail how it can be used to describe weak measurements and the surprising results they entail. We also discuss the limitations of von Neumann's model of measurements, and explain how they can be overcome with POVMs and Kraus operators. We provide the mathematical tools necessary to work with these generalized measurements and to derive master equations from them. Finally, we demonstrate how these can be applied in research problems by calculating the Quantum Zeno Effect.
In this manuscript we present a calculation of a physical observable in a non-perturbative quantum gravitational physical process from covariant Loop Quantum Gravity. The process regards the transition of a trapped region to an anti--trapped region, treated as a quantum geometry transition akin to gravitational tunneling. Figuratively speaking, this is a quantum transition of a black hole to a white hole. The physical observables are the characteristic timescales in which the process takes place. After an introduction, we begin with two chapters that review, define and extend main tools relevant to Lorentzian spinfoams and their semiclassical limit. We then dedicate a chapter to the classical exterior spacetime, which provides the setup for the problem. In the last two chapters, we arrive at an explicit, analytically well-defined and finite expression for a transition amplitude describing this process and use the semiclassical approximation to estimate the relevant amplitudes for an arbitrary choice of boundary conditions. We conclude that the transition is predicted to be allowed by LQG, with a characteristic duration that is linear in the mass, when the process takes place. The probability for the process to take place is exponentially suppressed but non-zero, resulting to a long lifetime.
The investigation of the behavior of both classical and quantum systems on non-Euclidean surfaces near the phase transition point represents an interesting research area of modern physics. In the case of classical spin systems, a generalization of the Corner Transfer Matrix Renormalization Group algorithm has been developed and successfully applied to spin models on infinitely many regular hyperbolic lattices. In this work, we extend these studies to specific types of lattices. It is important to say that no suitable algorithms for numerical analysis of ground-states of quantum systems in similar conditions have been implemented yet. In this work, we offer a particular solution by proposing a variational numerical algorithm Tensor Product Variational Formulation, which assumes a quantum ground-state written in the form of a low-dimensional uniform tensor product state. We apply the Tensor Product Variational Formulation to three typical quantum models on a variety of regular hyperbolic lattices. The main outcomes are the following: (1) We propose an algorithm for calculation and classification of the thermodynamic properties of the Ising model on triangular-tiled hyperbolic lattices. In addition, we investigate the origin of the mean-field universality on a series of weakly curved lattices. (2) We develop the Tensor Product Variational Formulation algorithm for the numerical analysis of the ground-state of the quantum systems on the hyperbolic lattices. (3) We study quantum phase transition phenomena for the three selected spin models on various types of the hyperbolic lattices including the Bethe lattice.
We present the concept which approaches the string theory to the field of time series forecast and data analysis through a transformation of currency rate data to the topology of physical strings and branes. We introduce new type of prediction models for financial time series based on string invariants. The performance of the first versions of prediction models is compared to support vector machines and artificial neural networks on an artificial and financial time series. We propose a string angular momentum as an another tool to analyze the stability of currency rates except the historical volatility. Next we investigate the fundamental properties of the space of time series data. We provide the proof that the space of time series data is a Kolmogorov space with T-0-separation axiom using the loop space of time series data.
One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several numerical simulation methods have been proposed in recent years. Amongst all of them, the Tensor Network algorithms have become increasingly popular in recent years, especially for their adaptability to simulate strongly correlated systems. The current work focuses on the generalization of such Tensor-Network-based algorithms, which are sufficiently robust to describe critical phenomena and phase transitions of multistate spin Hamiltonians in the thermodynamic limit. We have chosen two algorithms: the Corner Transfer Matrix Renormalization Group and the Higher-Order Tensor Renormalization Group. This work, based on tensor-network analysis, opens doors for the understanding of phase transition and entanglement of the interacting systems on the non-Euclidean geometries. We focus on three main topics: A new thermodynamic model of social influence, free energy is analyzed to classify the phase transitions on an infinite set of the negatively curved geometries where a relation between the free energy and the Gaussian radius of the curvature is conjectured, a unique tensor-based algorithm is proposed to study the phase transition on fractal structures.
In the current review, we study the model of quantum graphs. We focus mainly on the resonance properties of quantum graphs. We define resolvent and scattering resonances and show their equivalence. We present various results on the asymptotics of the number of resolvent resonances in both non-magnetic and magnetic quantum graphs and find bounds on the coefficient by the leading term of the asymptotics. We explain methods how to find the spectral and resonance condition. Most of the notions and theorems are illustrated in examples. We show how to find resonances numerically and, in a simple example, we find trajectories of resonances in the complex plane. We discuss Fermi's golden rule for quantum graphs and distribution of the mean intensity for the topological resonances.
Selected recent contributions involving fluctuating velocity fields to the rapidly developing domain of stochastic field theory are reviewed. Functional representations for solutions of stochastic differential equations and master equations are worked out in detail with an em- phasis on multiplicative noise and the inherent ambiguity of the functional method. Application to stochastic models of isotropic turbulence of multi-parameter expansions in regulators of dimensional and analytic renormalization is surveyed. Effects of the choice of the renormalization scheme are investigated. Special attention is paid to the role and properties of the minimal subtraction scheme. Analysis of the consequences of symmetry breaking of isotropic turbulence with the use of the renormalization-group method is demonstrated by the effects due to helicity, strong and weak anisotropy. A careful description is given of the influence of turbulent advection on paradigmatic reaction-diffusion problems.
In this review article three promising aspects of top quark production are discussed: the charge asymmetry in top quark pair production, the search for resonant top quark pair production, and electroweak single top quark production. First, an overview of the theoretical predictions of top quark pair and single top quark production is given. Then, for each topic the general analysis strategy and improvements are exemplarily explained using selected analyses and are put into the context of the global status at the beginning of LHC Run II and progress in this field. The example analyses discussed in more detail in this article use data from the LHC experiment CMS and for the charge asymmetry studies also data from the Tevatron experiment CDF have been used.
The article provides a tutorial review on how to treat Ising models within mean-field (MF), effective-field (EF) and exact methods. MF solutions of the spin-1 Blume-Capel (BC) model and the mixed-spin Ising model demonstrate a change of continuous phase transitions to discontinuous ones at a tricritical point. A quantum phase transition of the spin-S Ising model driven by a transverse field is explored within MF method. EF theory is elaborated within a single- and two-spin cluster approach to demonstrate an efficiency of this approximate method. The long-standing problem of this method concerned with a self-consistent determination of the free energy is addressed. EF theory is adapted for the spin-1/2 Ising model, the spin-S BC model and the transverse Ising model. The particular attention is paid to continuous and discontinuous transitions. Exact results for the spin-1/2 Ising chain, spin-1 BC chain and mixed-spin Ising chain are obtained using the transfer-matrix method, the crucial steps of which are reviewed for a spin-1/2 Ising square lattice. Critical points of the spin-1/2 Ising model on several lattices are rigorously obtained with the help of dual, star-triangle and decoration-iteration transformations. Mapping transformations are adapted to obtain exact results for the mixed-spin Ising model on planar lattices. An increase in the coordination number of the mixed-spin Ising model on decorated planar lattices gives rise to reentrant transitions, while the critical temperature of the mixed-spin Ising model on a regular honeycomb lattice is always greater than that of two semi-regular archimedean lattices. The effect of selective site dilution of the mixed-spin Ising model on a honeycomb lattice upon phase diagrams is examined. The review affords a brief account of the Ising models solved within MF, EF and exact methods along with a few comments on their future applicability.
The review deals with a generalization of the Rouse and Zimm bead-spring models of the dynamics of flexible polymers in dilute solutions. As distinct from these popular theories, the memory in the polymer motion is taken into account. The memory naturally arises as a consequence of the fluid and bead inertia within the linearized Navier-Stokes hydrodynamics. We begin with a generalization of the classical theory of the Brownian motion, which forms the basis of any theory of the polymer dynamics. The random force driving the Brownian particles is not the white one as in the Langevin theory, but "colored", i.e., statistically correlated in time, and the friction force on the particles depends on the history of their motion. An efficient method of solving the resulting generalized Langevin equations is presented and applied to the solution of the equations of motion of polymer beads. The memory effects lead to several peculiarities in the time correlation functions used to describe the dynamics of polymer chains. So, the mean square displacement of the polymer coils contains algebraic long-time tails and at short times it is ballistic. It is shown how these features reveal in the experimentally observable quantities, such as the dynamic structure factors of the scattering or the viscosity of polymer solutions. A phenomenological theory is also presented that describes the dependence of these quantities on the polymer concentration in solution.
This review is focused on the behavior of finite macroscopic systems (as opposed to infinitely large systems) determined from microscopic interactions. The temperature is assumed to be sufficiently below the critical point so that coexistence of two or more phases can occur and the systems can undergo first-order phase transitions. We summarize the rigorous results on the finite-size behavior for a specific but wide class of models of real systems-the lattice-gas models of dimension d >= 2 with a finite number of ground states for which the free energy density can be expressed via convergent cluster expansion series. The behavior is rather sensitive to the interaction of the system with its surroundings (boundary conditions). In addition to periodic boundary conditions, which is a very popular choice, weak boundary conditions are considered. The latter are much more realistic, although they rule out the presence of large interfaces or droplets (phase separation) in the systems. For boundary conditions so strong that phase separation is possible, the situation is very complex, and we provide rigorous results only for a two-dimensional Ising model. The majority of the paper, however, is devoted to an application of these finite-size results to an interesting phenomenon in electrochemistry in which first-order phase transitions may occur at metal-electrolyte interfaces as a result of the deposition of metals on surfaces of other, more noble metals at electric potentials above the Nernst threshold. This is called underpotential deposition (UPD), and, for example, copper or silver may be so deposited on a surface of gold or platinum. The presence of such transitions is associated with sharp spikes that are observed in the current vs. electric potential plots of UPD processes. The application of the finite-size results to this problem is not straightforward, for it must take into account a polycrystalline structure of the surfaces. In fact, for a single crystalline domain on the surface the theory predicts spikes that are two or more orders of magnitude taller and sharper than those observed in experiments. On the other hand, when the surface is modeled realistically as an ensemble of many crystalline domains whose individual contributions are summed up to produce an overall spike, the agreement with experiment can be rather accurate. This is demonstrated in detail for two experimental spikes associated with UPD of copper on the (111) surface of platinum and gold electrodes.
It is important to understand properties of different materials and the impact they have on devices used in communication networks. This paper is an overview of optical non-linearities in Silicon and Gallium Nitride and how these nonlinearities can be used in the realization of optical ultra-fast devices targeting the next generation integrated optics. Research results related to optical lasing, optical switching, data modulation, optical signal amplification and photo-detection using Gallium Nitride devices based on waveguides are examined. Attention is also paid to hybrid and monolithic integration approaches towards the development of advanced photonic chips.
This paper provides an examination of how are prediction of standard quantum mechanic (QM) affected by introducing a noncommutative (NC) structure into the configuration space of the considered system (electron in the Coulomb potential in the present case). The parameter controlling the extent of modification is denoted as {\lambda}. The coordinates in the NC space are realized via creation and annihilation operators acting in an auxiliary Fock space, this one being chosen in such a way that the rotational invariance of the system remains intact also in NCQM. Analog of Schr\odinger equation for hydrogen atom is found and analytically solved, both for bound states and scattering. The exact formulas for NC corrections are given. None of the NC predictions contradicts experimentally verified QM results, since in the correspondence limit {\lambda} -> 0 both QM and NCQM coincide. Highly surprising feature of the NC version is the existence of bound states for repulsive potential at ultra-high energies. However, these disappear from the Hilbert space in the mentioned limit. The whole problem is solved also using a method analogous to that of Pauli. Besides rotational invariance, the dynamical symmetry related to the conservation of NC analog of Laplace-Runge-Lenz vector is being used and the results obtained this way are in the full agreement with those given by Schr\odinger-like approach. The presented NC deformation of QM preserves all those mysterious properties of the Coulomb system that made it a distinguished key-stone of the modern physics.
We present an analysis of two different approximations to the scalar field theory on the fuzzy sphere, a nonperturbative and a perturbative one, which are both multitrace matrix models. We show that the former reproduces a phase diagram with correct features in a qualitative agreement with the previous numerical studies and that the latter gives a phase diagram with features not expected in the phase diagram of the field theory.
Theoretical predictions of noncovalent interaction energies, important e.g. in drug-design or design of hydrogen-storage materials, belong to grand-challenges of contemporary quantum chemistry. In this respect, quantum Monte Carlo (QMC) approaches based on the fixed-node diffusion Monte Carlo (FN-DMC), provide a promising alternative to the commonly used coupled-cluster (CC) methods for their benchmark accuracy, massive parallelism, and favorable scaling. The current tutorial review provides a brief state-of-the-art overview of QMC in ab initio quantum chemical calculations of noncovalent interaction energies, covering recent advances in this field: computational protocols based on FN-DMC with single Slater determinant guiding functions, range of their applicability, tradeoffs, analysis of the success of this simple approach in weakly bound molecular complexes and other related topics. The review is supplemented by an easy-to-grasp practical and detailed tutorial on calculation of molecular interaction energies using a free quantum chemical software (GAMESS, QWalk). This part thus provides an accessible starting point for the readers interested in practical calculations.
Optical metrology methods are an integral part of experimental mechanics. In this communication a systematic study of a variety of these methods is presented concerning the origin and subsequent development over the following period of a few decades. Particularly, the advancement of coherent light imaging in the field of diffraction optics based measuring procedures is described. Primarily, holographic/speckle interferometry used in surface deformation measurements in deformable body mechanics is treated from the viewpoint of optical scheme optimization. Topics such as image plane holography, pulsed ruby laser holography, electronic speckle pattern interferometry (ESPI) and double-channel speckle interferometry, hybrid experimental-numerical stress state analysis, light diffraction testing of surface roughness are discussed as well as their primary applications. Theoretical fundamentals and conditions for realization of each method are shown. The main aim of this study is to point out the basic features and potential exploitation of physical phenomena which are related to interference and diffraction of coherent light.
The latest experimental results concerning the top quark physics obtained by the experiments at Large Hadron Colliders using the data produced in proton-proton collisions at root s = 7 and 8 TeV are shown. The data were collected by the ATLAS detector in 2011 (7 TeV) and 2012 (8 TeV) with the integrated luminosity of 4.9 fb(-1) and 21 fb(-1) and the CMS detector at the same collision energies with the integrated luminosity of 5 fb(-1) and 20 fb(-1), respectively. The results on different aspects of the top quark studies including searches of physics beyond the Standard Model are also reported. No signs of physics beyond the Standard Model has been found so far.
Randomness is an invaluable resource in today's life with a broad use reaching from numerical simulations through randomized algorithms to cryptography. However, on the classical level no true randomness is available and even the use of simple quantum devices in a prepare-measure setting suffers from lack of stability and controllability. This gave rise to a group of quantum protocols that provide randomness certified by classical statistical tests - Device Independent Quantum Random Number Generators. In this paper we review the most relevant results in this field, which allow the production of almost perfect randomness with help of quantum devices, supplemented with an arbitrary weak source of additional randomness. This is in fact the best one could hope for to achieve, as with no starting randomness (corresponding to no free will in a different concept) even a quantum world would have a fully deterministic description.
Improvements in numerical ocean models and more and better observations have made the gaps between the two all the more apparent. In a recent resurgence in the study of turbulence due to wave orbital motion, some scholars have sought to address part of the problem by proposing the mechanism as an important missing part from vertical mixing models. Yet the subject remains contentious. This review is an attempt to bring together in one place the main results and insights from almost a century of scholarly discourse on the subject, demonstrating the breadth of ideas therein, as well as highlighting some of the outstanding problems.
