Abstract: Topological phases of materials are characterized by topological invariants that are conventionally calculated by different means according to the dimension and symmetry class of the system. For topological materials described by Dirac models, we introduce a wrapping number as a unified approach to obtain the topological invariants in arbitrary dimensions and symmetry classes. Given a unit vector that parametrizes the momentum dependence of the Dirac model, the wrapping number describes the degree of the map from the Brillouin zone torus to the sphere formed by the unit vector that we call the Dirac sphere. This method is gauge-invariant and originates from the intrinsic features of the Dirac model and moreover places all known topological invariants, such as the Chern number, winding number, Pfaffian, etc, on equal footing.
Abstract: We study the simulation of the topological phases in three subsequent dimensions with quantum walks. We focus mainly on the completion of a table for the protocols of the quantum walk that could simulate different families of the topological phases in one, two, and three dimensions. We also highlight the possible boundary states that can be observed for each protocol in different dimensions and extract the conditions for their emergences. To further enrich the simulation of the topological phenomena, we include step-dependent coins in the evolution operators of the quantum walks. This leads to step dependence of the simulated topological phenomena and their properties which introduces dynamicity as a feature of simulated topological phases and boundary states. This dynamicity provides the step number of the quantum walk as a means to control and engineer the numbers of topological phases and boundary states, their numbers, types, and even occurrences.
Friedrich-Schiller-Universität Jena, Physikalisch-Astronomische Fakultät (2021)
Abstract: Discrete-time quantum walks are among the branches of quantum information and computation. They are platforms for developing quantum algorithms for quantum computers. In addition, due to their universal primitive nature, discrete-time quantum walks have been used to simulate other quantum systems and phenomena that are observed in physics and chemistry. To fully utilize the potentials that the discrete-time quantum walks hold in their applications, control over the discrete-time quantum walks and their properties becomes essential. In this dissertation, we propose two models for attaining a high level of control over the discrete-time quantum walks. In the first one, we incorporate a dynamical nature for the unitary operator performing the quantum walks. This enables us to readily control the properties of the walker and produce diverse behaviors for it. We show that with our proposal, the important properties of the discrete-time quantum walks such as variance would indeed improve. To explore the potential of this proposal, we apply it in the simulations of topological phases in condensed matter physics. With our proposal, we can control the simulations and determine the type of topological phenomena that should be simulated. In addition, we confirm simulations of topological phases and boundary states that can be observed in one-, two- and three-dimensional systems. Finally, we report the emergence of exotic phase structures in form of cell-like structures that contain all types of topological phases and boundary states of certain classes. In our second proposal, we take advantage of resources available in quantum mechanics, namely quantum entanglement and entangled qubits. In this proposal, we use entangled qubits in the structure of a quantum walk and show that by tuning the initial entanglement between these qubits and how these qubits are modified through the walk, one is able to produce diverse behaviors for the quantum walk and control its behavior.
Abstract: In order to classify and understand structure of the spacetime, investigation of the geodesic motions of massive and massless particles is a key tool. So the geodesic equation is a central equation of gravitating systems and the subject of geodesics in the black hole dictionary attracted much attention. In this paper, we give a full description of geodesic motions in three-dimensional spacetime. We investigate the geodesics near charged BTZ black holes and then generalize our prescriptions to the case of massive gravity. We show that electric charge is a critical parameter for categorizing the geodesic motions of both lightlike and timelike particles. In addition, we classify the type of geodesics based on the particle properties and geometry of spacetime.
Abstract: In this paper, we investigate the thermodynamics of dyonic black holes in the presence of Born-Infeld electromagnetic field. We show that electric-magnetic duality reported for dyonic solutions with Maxwell field is omitted in case of Born-Infeld generalization. We also confirm that generalization to nonlinear field provides the possibility of canceling the effects of cosmological constant. This is done for nonlinearity parameter with 10−33 eV2 order of magnitude which is high nonlinearity regime. In addition, we show that for small electric/magnetic charge and high nonlinearity regime, black holes would develop critical behavior and several phases. In contrast, for highly charged case and Maxwell limits (small nonlinearity), black holes have one thermal stable phase. We also find that the pressure of the cold black holes is bounded by some constraints on its volume while hot black holes' pressure has physical behavior for any volume. In addition, we report on possibility of existences of triple point and reentrant of phase transition in thermodynamics of these black holes. Finally, we show that if electric and magnetic charges are identical, the behavior of our solutions would be Maxwell like (independent of nonlinear parameter and field). In other words, nonlinearity of electromagnetic field becomes evident only when these black holes are charged magnetically and electrically different.
Abstract: Quantum walks are versatile simulators of topological phases and phase transitions as observed in condensed-matter physics. Here, we utilize a step-dependent coin in quantum walks and investigate what topological phases we can simulate with it, their topological invariants, bound states, and possibility of phase transitions. These quantum walks simulate nontrivial phases characterized by topological invariants (winding number) ±1, which are similar to the ones observed in topological insulators and polyacetylene. We confirm that the number of phases and their corresponding bound states increase step dependently. In contrast, the size of topological phase and distance between two bound states are decreasing functions of steps resulting into formation of multiple phases as quantum walks proceed (multiphase configuration). We show that, in the bound states, the winding number and group velocity are ill defined and the second moment of the probability density distribution in position space undergoes an abrupt change. Therefore, there are phase transitions taking place over the bound states and between two topological phases with different winding numbers.
Abstract: One of the major open problems in theoretical physics is the lack of a consistent quantum gravity theory. Recent developments in our knowledge on thermodynamic phase transitions of black holes and their van der Waals-like behavior may provide an interesting quantum interpretation of classical gravity. Studying different methods of investigating phase transitions can extend our understanding of the nature of quantum gravity. In this paper, we present an alternative theoretical approach for finding thermodynamic phase transitions in the extended phase space. Unlike the standard methods based on the usual equation of state involving temperature, our approach uses a new quasi-equation constructed from the slope of temperature versus entropy. This approach addresses some of the shortcomings of the other methods and provides a simple and powerful way of studying the critical behavior of a thermodynamical system. Among the applications of this approach, we emphasize the analytical demonstration of possible phase transition points and the identification of the non-physical range of horizon radii for black holes.
Abstract: In this paper, we investigate thermodynamical structure of dyonic black holes in the presence of gravity's rainbow. We confirm that for super magnetized and highly pressurized scenarios, the number of black holes' phases is reduced to a single phase. In addition, due to specific coupling of rainbow functions, it is possible to track the effects of temporal and spatial parts of our setup on thermodynamical quantities/behaviors including equilibrium point, existence of multiple phases, possible phase transitions and conditions for having a uniform stable structure.
Abstract: Regarding the significant interests in massive gravity and combining it with gravity's rainbow and also BTZ black holes, we apply the formalism introduced by Jiang and Han in order to investigate the quantization of the entropy of black holes. We show that the entropy of BTZ black holes in massive gravity's rainbow is quantized with equally spaced spectra and it depends on the black holes' properties including massive parameters, electrical charge, the cosmological constant, and also rainbow functions. In addition, we show that quantization of the entropy results in the appearance of novel properties for this quantity, such as the existence of divergences, non-zero entropy in a vanishing horizon radius, and the possibility of tracing out the effects of the black holes' properties. Such properties are absent in the non-quantized version of the black hole entropy. Furthermore, we investigate the effects of quantization on the thermodynamical behavior of the solutions. We confirm that due to quantization, novel phase transition points are introduced and stable solutions are limited to only de Sitter black holes (anti-de Sitter and asymptotically flat solutions are unstable).
Abstract: Motivated by the string theory corrections in the low-energy limit of both gauge and gravity sides, we consider three-dimensional black holes in the presence of dilatonic gravity and the Born-Infeld nonlinear electromagnetic field. We find that geometric behavior of the solutions is similar to the behavior of the hyperscaling violation metric, asymptotically. We also investigate thermodynamics of the solutions and show that the generalization to dilatonic gravity introduces novel properties into thermodynamics of the black holes which were absent in the Einstein gravity. Furthermore, we explore the possibility of tuning out part of the dilatonic effects using the Born-Infeld generalization.
Abstract: Quantum fluctuation effects have an irrefutable role in high-energy physics. Such fluctuation can be often regarded as a correction of the infrared (IR) limit. In this paper, the effects of the first-order correction of entropy, caused by thermal fluctuation, on the thermodynamics of charged black holes in gravity’s rainbow will be discussed. It will be shown that such correction has profound contributions to the high-energy limit of thermodynamical quantities and the stability conditions of black holes, and, interestingly, has no effect on thermodynamical phase transitions. The coupling between gravity’s rainbow and the first-order correction will be addressed. In addition, the measurement of entropy as a function of fluctuation of temperature will be covered, and it will be shown that the de Sitter case enforces an upper limit on the values of temperature and produces cyclic-like diagrams, while for the anti-de Sitter case, a lower limit on the entropy is provided; although for special cases a cyclic-like behavior could be observed, no upper or lower limit exists for the temperature. In addition, a comparison between non-correction and correction-included cases on the thermodynamical properties of solutions will also be discussed and the effects of the first-order correction will be highlighted. It will be shown that the first-order correction provides solutions with larger classes of thermal stability conditions, which may result in the existence of a larger number of thermodynamical structures for the black holes.
Abstract: We report on the possibility of controlling quantum random walks (QWs) with a step-dependent coin (SDC). The coin is characterized by a (single) rotation angle. Considering different rotation angles, one can find diverse probability distributions for this walk including: complete localization, Gaussian and asymmetric likes. In addition, we explore the entropy of walk in two contexts; for probability density distributions over position space and walker's internal degrees of freedom space (coin space). We show that entropy of position space can decrease for a SDC with the step-number, quite in contrast to a walk with step-independent coin (SIC). For entropy of coin space, a damped oscillation is found for walk with SIC while for a SDC case, the behavior of entropy depends on rotation angle. In general, we demonstrate that quantum walks with simple initiatives may exhibit a quite complex and varying behavior if SDCs are applied. This provides the possibility of controlling QW with a SDC.
Abstract: The paper at hand studies the heat engine provided by black holes in the presence of massive gravity. The main motivation is to investigate the effects of massive gravity on different properties of the heat engine. It will be shown that massive gravity parameters modify the efficiency of engine on a significant level. Furthermore, it will be pointed out that it is possible to have a heat engine for non-spherical black holes in massive gravity, and therefore, we will study the effects of horizon topology on the properties of heat engine. Surprisingly, it will be shown that the highest efficiency for the heat engine belongs to black holes with the hyperbolic horizon, while the lowest one belongs to the spherical black holes.
Abstract: The solutions of U(1) gauge-gravity coupling is one of the interesting models for analyzing the semi-classical nature of spacetime. In this regard, different well-known singular and nonsingular solutions have been taken into account. The paper at hand investigates the geometrical properties of the magnetic solutions by considering Maxwell and power Maxwell invariant (PMI) nonlinear electromagnetic fields in the context of massive gravity. These solutions are free of curvature singularity, but have a conic one which leads to presence of deficit/surplus angle. The emphasize is on modifications that these generalizations impose on deficit angle which determine the total geometrical structure of the solutions, hence, physical/gravitational properties. It will be shown that depending on the background spacetime [being anti de Sitter (AdS) or de Sitter (dS)], these generalizations present different effects and modify the total structure of the solutions differently.
Abstract: Motivated by recent progresses in the field of massive gravity, the paper at hand investigates the thermodynamical structure of black holes with three specific generalizations: i) Gauss-Bonnet gravity which is motivated from string theory ii) PMI nonlinear electromagnetic field which is motivated from perspective of the QED correction iii) massive gravity which is motivated by obtaining the modification of standard general relativity. The exact solutions of this setup are extracted which are interpreted as black holes. In addition, thermodynamical quantities of the solutions are calculated and their critical behavior are studied. It will be shown that although massive and Gauss-Bonnet gravities are both generalizations in gravitational sector, they show opposing effects regarding the critical behavior of the black holes. Furthermore, a periodic effect on number of the phase transition is reported for variation of the nonlinearity parameter and it will be shown that for super charged black holes, system is restricted in a manner that prevents it to reach the critical point and to acquire phase transition. In addition, the effects of geometrical structure on thermodynamical phase transition will be highlighted.
Abstract: The Noble Prize in physics 2016 motivates one to study different aspects of topological properties and topological defects as their related objects. Considering the significant role of the topological defects (especially magnetic strings) in cosmology, here, we will investigate three dimensional horizonless magnetic solutions in the presence of two generalizations: massive gravity and nonlinear electromagnetic field. The effects of these two generalizations on properties of the solutions and their geometrical structure are investigated. The differences between de Sitter and anti de Sitter solutions are highlighted and conditions regarding the existence of phase transition in geometrical structure of the solutions are studied.
Abstract: This paper is devoted to an investigation of nonlinearly charged dilatonic black holes in the context of gravity's rainbow with two cases: (1) by considering the usual entropy, (2) in the presence of first order logarithmic correction of the entropy. First, exact black hole solutions of dilatonic Born--Infeld gravity with an energy dependent Liouville-type potential are obtained. Then, thermodynamic properties of the mentioned cases are studied, separately. It will be shown that although mass, entropy and the heat capacity are modified due to the presence of a first order correction, the temperature remains independent of it. Furthermore, it will be shown that divergences of the heat capacity, hence phase transition points are also independent of a first order correction, whereas the stability conditions are highly sensitive to variation of the correction parameter. Except for the effects of a first order correction, we will also present a limit on the values of the dilatonic parameter and show that it is possible to recognize AdS and dS thermodynamical behaviors for two specific branches of the dilatonic parameter. In addition, the effects of nonlinear electromagnetic field and energy functions on the thermodynamical behavior of the solutions will be highlighted and dependency of critical behavior, on these generalizations will be investigated.
Abstract: Magnetic branes of Gauss–Bonnet–Maxwell theory in the context of massive gravity is studied in detail. Exact solutions are obtained and their interesting geometrical properties are investigated. It is argued that although these horizonless solutions are free of curvature singularity, they enjoy a cone-like geometry with a conic singularity. In order to investigate the effects of various parameters on the geometry of conic singularity, its corresponding deficit angle is studied. It will be shown that despite the effects of Gauss–Bonnet gravity on the solutions, deficit angle is free of Gauss–Bonnet parameter. On the other hand, the effects of massive gravity, cosmological constant and electrical charge on the deficit angle will be explored. Also, a brief discussion related to possible geometrical phase transition of these topological objects is given.