Showing papers on "Dissipative system published in 2020"

Variational Quantum Simulation of General Processes.

Abstract: Variational quantum algorithms have been proposed to solve static and dynamic problems of closed many-body quantum systems. Here we investigate variational quantum simulation of three general types of tasks-generalized time evolution with a non-Hermitian Hamiltonian, linear algebra problems, and open quantum system dynamics. The algorithm for generalized time evolution provides a unified framework for variational quantum simulation. In particular, we show its application in solving linear systems of equations and matrix-vector multiplications by converting these algebraic problems into generalized time evolution. Meanwhile, assuming a tensor product structure of the matrices, we also propose another variational approach for these two tasks by combining variational real and imaginary time evolution. Finally, we introduce variational quantum simulation for open system dynamics. We variationally implement the stochastic Schrodinger equation, which consists of dissipative evolution and stochastic jump processes. We numerically test the algorithm with a 6-qubit 2D transverse field Ising model under dissipation.

Tenfold Way for Quadratic Lindbladians.

Abstract: We uncover a topological classification applicable to open fermionic systems governed by a general class of Lindblad master equations. These ``quadratic Lindbladians'' can be captured by a non-Hermitian single-particle matrix which describes internal dynamics as well as system-environment coupling. We show that this matrix must belong to one of ten non-Hermitian Bernard-LeClair symmetry classes which reduce to the Altland-Zirnbauer classes in the closed limit. The Lindblad spectrum admits a topological classification, which we show results in gapless edge excitations with finite lifetimes. Unlike previous studies of purely Hamiltonian or purely dissipative evolution, these topological edge modes are unconnected to the form of the steady state. We provide one-dimensional examples where the addition of dissipators can either preserve or destroy the closed classification of a model, highlighting the sensitivity of topological properties to details of the system-environment coupling.

Novel Physical Insights into the Thermodynamic Irreversibilities Within Dissipative EMHD Fluid Flows Past over a Moving Horizontal Riga Plate in the Coexistence of Wall Suction and Joule Heating Effects: A Comprehensive Numerical Investigation

Abstract: In the case of an electro-magneto-hydrodynamic actuator, little is known about the thermo-magneto-hydrodynamic irreversibilities arising in the dissipative flows of weakly conducting fluids past over a moving Riga plate. In this study, the electro-magneto-hydrodynamic convective flow features of a viscous electrically conducting fluid over a horizontal Riga plate are deliberated comprehensively by considering the wall suction and Joule heating effects. It is assumed that the permanent magnets are of equal width and mounted alternatively on a plane surface. Due to the electromagnetic proprieties of the Riga plate, the exponentially decaying Grinberg term is included in the momentum conservation equation as a resistive drag force in this investigation. The modeled differential equations were non-dimensionalized and simplified mathematically by utilizing suitable dimensionless variables and adopting admissible physical assumptions. Numerical solutions were established herein by utilizing an efficient algorithm based on the generalized differential quadrature method and the Newton–Raphson iterative technique. It is worth concluding that the presence of the wall suction effect enhances noticeably the heat transfer rate and its thermodynamic irreversibility near the Riga plate, while a reverse feature is depicted with the elevating strengths of the magnetization field.

Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos

Abstract: Mathematical tools for distinguishing open quantum systems that are chaotic from those that are exactly solvable fill an important gap in understanding dissipation and decoherence in scenarios relevant to quantum-based technologies.

Trainability of Dissipative Perceptron-Based Quantum Neural Networks

Abstract: Several architectures have been proposed for quantum neural networks (QNNs), with the goal of efficiently performing machine learning tasks on quantum data. Rigorous scaling results are urgently needed for specific QNN constructions to understand which, if any, will be trainable at a large scale. Here, we analyze the gradient scaling (and hence the trainability) for a recently proposed architecture that we called dissipative QNNs (DQNNs), where the input qubits of each layer are discarded at the layer's output. We find that DQNNs can exhibit barren plateaus, i.e., gradients that vanish exponentially in the number of qubits. Moreover, we provide quantitative bounds on the scaling of the gradient for DQNNs under different conditions, such as different cost functions and circuit depths, and show that trainability is not always guaranteed.

Tunable Nonreciprocal Quantum Transport through a Dissipative Aharonov-Bohm Ring in Ultracold Atoms.

Abstract: We report the experimental observation of tunable, nonreciprocal quantum transport of a Bose-Einstein condensate in a momentum lattice. By implementing a dissipative Aharonov-Bohm (AB) ring in momentum space and sending atoms through it, we demonstrate a directional atom flow by measuring the momentum distribution of the condensate at different times. While the dissipative AB ring is characterized by the synthetic magnetic flux through the ring and the laser-induced loss on it, both the propagation direction and transport rate of the atom flow sensitively depend on these highly tunable parameters. We demonstrate that the nonreciprocity originates from the interplay of the synthetic magnetic flux and the laser-induced loss, which simultaneously breaks the inversion and the time-reversal symmetries. Our results open up the avenue for investigating nonreciprocal dynamics in cold atoms, and highlight the dissipative AB ring as a flexible building element for applications in quantum simulation and quantum information.

Extended dissipative synchronization for semi-Markov jump complex dynamic networks via memory sampled-data control scheme

Abstract: The work is concerned with the synchronization issue of complex dynamic networks subject to the semi-Markov process. The semi-Markov process is used to describe the switching among different modes of network topology. Meanwhile, a constant signal transmission delay is considered in the sampled-data controller when dealing with the synchronization problem. The main purpose is to design a novel memory sampled-data control scheme to ensure the synchronization of the master-slave system. With the help of some improved integral inequality techniques, several sufficient conditions are obtained to assure the error system achieves the stochastic stability and satisfies an extended dissipative performance index via constructing Lyapunov function. Finally, two simulation examples are given to verify the validity and superiority of the memory sampled-data controller designed.

Stability of the isotropic pressure condition

Abstract: We investigate the conditions for the (in)stability of the isotropic pressure condition in collapsing spherically symmetric, dissipative fluid distributions. It is found that dissipative fluxes, and/or energy density inhomogeneities and/or the appearance of shear in the fluid flow, force any initially isotropic configuration to abandon such a condition, generating anisotropy in the pressure. To reinforce this conclusion we also present some arguments concerning the axially symmetric case. The consequences ensuing our results are analyzed.

Dissipative Filtering for Switched Fuzzy Systems With Missing Measurements

Abstract: This paper investigates the dissipative filtering problem for a class of discrete-time switched fuzzy systems with missing measurements. The fuzzy plant under consideration incorporates characteristics of Takagi–Sugeno fuzzy systems and switched systems simultaneously. The occurrence of missing measurements is described by a stochastic variable that satisfies the Bernoulli binary distribution, which characterizes the effect of data loss in information transmission between the plant and the filter. Utilizing the Lyapunov function technique, sufficient conditions are developed to ensure that the resultant filtering error system is exponentially stable and strictly dissipative. Two simulation examples are presented to illustrate the validity of the proposed method.

Memristor initial-boosted coexisting plane bifurcations and its extreme multi-stability reconstitution in two-memristor-based dynamical system

Abstract: Initial-dependent extreme multi-stability and offset-boosted coexisting attractors have been significantly concerned recently. This paper constructs a novel five-dimensional (5-D) two-memristor-based dynamical system by introducing two memristors with cosine memductance into a three-dimensional (3-D) linear autonomous dissipative system. Through theoretical analyses and numerical plots, the memristor initial-boosted coexisting plane bifurcations are found and the memristor initial-dependent extreme multi-stability is revealed in such a two-memristor-based dynamical system with plane equilibrium. Furthermore, a dimensionality reduction model with the determined equilibrium is established via an integral transformation method, upon which the memristor initial-dependent extreme multi-stability is reconstituted theoretically and expounded numerically. Finally, physically circuit-implemented PSIM (power simulation) simulations are carried out to validate the plane offset-boosted coexisting behaviors.

Non-Hermitian linear response theory

Abstract: Linear response theory lies at the heart of studying quantum matters, because it connects the dynamical response of a quantum system to an external probe to correlation functions of the unprobed equilibrium state. Thanks to linear response theory, various experimental probes can be used for determining equilibrium properties. However, so far, both the unprobed system and the probe operator are limited to Hermitian ones. Here, we develop a non-Hermitian linear response theory that considers the dynamical response of a Hermitian system to a non-Hermitian probe, and we can also relate such a dynamical response to the properties of an unprobed Hermitian system at equilibrium. As an application of our theory, we consider the real-time dynamics of momentum distribution induced by one-body and two-body dissipations. Remarkably, for a critical state with no well-defined quasi-particles, we find that the dynamics are slower than the normal state with well-defined quasi-particles, and our theory provides a model-independent way to extract the critical exponent in the real-time correlation function. We find surprisingly good agreement between our theory and a recent cold atom experiment on the dissipative Bose–Hubbard model. We also propose to further quantitatively verify our theory by performing experiments on dissipative one-dimensional Luttinger liquid. Generalization of linear response theory to the non-Hermitian case turns dissipation into a new tool for detecting equilibrium phases. The prediction from this theory remarkably agrees with a recent cold atom experiment.

On the relation between enhanced dissipation time-scales and mixing rates

Abstract: We study diffusion and mixing in different linear fluid dynamics models, mainly related to incompressible flows. In this setting, mixing is a purely advective effect which causes a transfer of energy to high frequencies. When diffusion is present, mixing enhances the dissipative forces. This phenomenon is referred to as enhanced dissipation, namely the identification of a time-scale faster than the purely diffusive one. We establish a precise connection between quantitative mixing rates in terms of decay of negative Sobolev norms and enhanced dissipation time-scales. The proofs are based on a contradiction argument that takes advantage of the cascading mechanism due to mixing, an estimate of the distance between the inviscid and viscous dynamics, and of an optimization step in the frequency cut-off. Thanks to the generality and robustness of our approach, we are able to apply our abstract results to a number of problems. For instance, we prove that contact Anosov flows obey logarithmically fast dissipation time-scales. To the best of our knowledge, this is the first example of a flow that induces an enhanced dissipation time-scale faster than polynomial. Other applications include passive scalar evolution in both planar and radial settings and fractional diffusion.

Unconventional Singularity in Anti-Parity-Time Symmetric Cavity Magnonics

Abstract: By engineering an anti-parity-time (anti-PT) symmetric cavity magnonics system with precise eigenspace controllability, we observe two different singularities in the same system. One type of singularity, the exceptional point (EP), is produced by tuning the magnon damping. Between two EPs, the maximal coherent superposition of photon and magnon states is robustly sustained by the preserved anti-PT symmetry. The other type of singularity, arising from the dissipative coupling of two antiresonances, is an unconventional bound state in the continuum (BIC). At the settings of BICs, the coupled system exhibits infinite discontinuities in the group delay. We find that both singularities coexist at the equator of the Bloch sphere, which reveals a unique hybrid state that simultaneously exhibits the maximal coherent superposition and slow light capability.

Distributed Dissipative State Estimation for Markov Jump Genetic Regulatory Networks Subject to Round-Robin Scheduling

Abstract: The distributed dissipative state estimation issue of Markov jump genetic regulatory networks subject to round-robin scheduling is investigated in this paper. The system parameters randomly change in the light of a Markov chain. Each node in sensor networks communicates with its neighboring nodes in view of the prescribed network topology graph. The round-robin scheduling is employed to arrange the transmission order to lessen the likelihood of the occurrence of data collisions. The main goal of the work is to design a compatible distributed estimator to assure that the distributed error system is strictly $(\Lambda _{1},\Lambda _{2},\Lambda _{3}) $ - $\gamma $ -stochastically dissipative. By applying the Lyapunov stability theory and a modified matrix decoupling way, sufficient conditions are derived by solving some convex optimization problems. An illustrative example is given to verify the validity of the provided method.

Measurement-induced transitions of the entanglement scaling law in ultracold gases with controllable dissipation

Abstract: Recent studies of quantum circuit models have theoretically shown that frequent measurements induce a transition in a quantum many-body system, which is characterized by a change in the scaling law of the entanglement entropy from a volume law to an area law. In order to propose a way to experimentally observe this measurement-induced transition, we present numerical analyses using matrix-product states on the quench dynamics of a dissipative Bose-Hubbard model with controllable two-body losses, which has been realized in recent experiments with ultracold atoms. We find that when the strength of dissipation increases, there occurs a measurement-induced transition from volume-law scaling to area-law scaling with a logarithmic correction in a region of relatively small dissipation. We also find that the strong dissipation leads to a revival of the volume-law scaling due to a continuous quantum Zeno effect. We show that dynamics starting with the area-law states exhibits strong suppression of particle transport stemming from ergodicity breaking, which can be used in experiments to distinguish them from the volume-law states.

Binary chemical reaction with activation energy in dissipative flow of non-Newtonian nanomaterial

Abstract: This paper deals with the entropy optimization and heat transport of magneto-nanomaterial flow of non-Newtonian (Jeffrey fluid) towards a curved stretched surface. MHD fluid is accounted. The model...

Viscoelastic hydrodynamics and holography

Abstract: We formulate the theory of nonlinear viscoelastic hydrodynamics of anisotropic crystals in terms of dynamical Goldstone scalars of spontaneously broken translational symmetries, under the assumption of homogeneous lattices and absence of plastic deformations. We reformulate classical elasticity effective field theory using surface calculus in which the Goldstone scalars naturally define the position of higher-dimensional crystal cores, covering both elastic and smectic crystal phases. We systematically incorporate all dissipative effects in viscoelastic hydrodynamics at first order in a long-wavelength expansion and study the resulting rheology equations. In the process, we find the necessary conditions for equilibrium states of viscoelastic materials. In the linear regime and for isotropic crystals, the theory includes the description of Kelvin-Voigt materials. Furthermore, we provide an entirely equivalent description of viscoelastic hydrodynamics as a novel theory of higher-form superfluids in arbitrary dimensions where the Goldstone scalars of partially broken generalised global symmetries play an essential role. An exact map between the two formulations of viscoelastic hydrodynamics is given. Finally, we study holographic models dual to both these formulations and map them one-to-one via a careful analysis of boundary conditions. We propose a new simple holographic model of viscoelastic hydrodynamics by adopting an alternative quantisation for the scalar fields.

Soliton dynamics in a fractional complex Ginzburg-Landau model

Abstract: The general objective of the work is to study dynamics of dissipative solitons in the framework of a one-dimensional complex Ginzburg-Landau equation (CGLE) of a fractional order. To estimate the shape of solitons in fractional models, we first develop the variational approximation for solitons of the fractional nonlinear Schrodinger equation (NLSE), and an analytical approximation for exponentially decaying tails of the solitons. Proceeding to numerical consideration of solitons in fractional CGLE, we study, in necessary detail, effects of the respective Levy index (LI) on the solitons’ dynamics. In particular, dependence of stability domains in the model's parameter space on the LI is identified. Pairs of in-phase dissipative solitons merge into single pulses, with the respective merger distance also determined by LI.

An effective two-dimensional model for MHD flows with transverse magnetic field

Abstract: This paper presents a model for quasi two-dimensional MHD flows between two planes with small magnetic Reynolds number and constant transverse magnetic field orthogonal to the planes. A method is presented that allows to take 3D effects into account in a 2D equation of motion thanks to a model for the transverse velocity profile. The latter is obtained by using a double perturbation asymptotic development both in the core flow and in the Hartmann layers arising along the planes. A new model is thus built that describes inertial effects in these two regions. Two separate classes of phenomena are thus pointed out : the one related to inertial effects in the Hartmann layer gives a model for recirculating flows and the other introduces the possibility of having a transverse dependence of the velocity profile in the core flow. The ''recirculating'' velocity profile is then introduced in the transversally averaged equation of motion in order to provide an effective 2D equation of motion. Analytical solutions of this model are obtained for two experimental configurations : isolated vortices aroused by a point electrode and axisymmetric parallel layers occurring in the MATUR (MAgneticTURbulence) experiment. The theory is found to give a satisfactory agreement with the experiment so that it can be concluded that recirculating flows are actually responsible for both vortices core spreading and excessive dissipative behavior of the axisymmetric side wall layers.

Dissipative couplings in cavity magnonics

Abstract: Cavity magnonics is an emerging field that studies the strong coupling between cavity photons and collective spin excitations such as magnons. This rapidly developing field connects some of the most exciting branches of modern physics, such as quantum information and quantum optics, with one of the oldest sciences on Earth, the magnetism. The past few years have seen a steady stream of exciting experiments that demonstrate novel magnon-based transducers and memories. Most of such cavity magnonic devices rely on coherent coupling that stems from the direct dipole–dipole interaction. Recently, a distinct dissipative magnon–photon coupling was discovered. In contrast to coherent coupling that leads to level repulsion between hybridized modes, dissipative coupling results in level attraction. It opens an avenue for engineering and harnessing losses in hybrid systems. This article gives a brief review of this new frontier. Experimental observations of level attraction are reviewed. Different microscopic mechanisms are compared. Based on such experimental and theoretical reviews, we present an outlook for developing open cavity systems by engineering and harnessing dissipative couplings.

Dissipative Fuzzy Tracking Control for Nonlinear Networked Systems With Quantization

Abstract: In this paper, the quantized static output feedback dissipative tracking control problem is considered for a class of discrete-time nonlinear networked systems based on Takagi–Sugeno fuzzy model approach. The measurement output of the system, the output of the reference model, and the control input signals will be quantized by static quantizers before them being transmitted to the controller and the plant, respectively. The attention of this paper is focused on the design of the static output feedback tracking controller to asymptotically stabilize the nonlinear networked system and achieve strictly dissipative tracking performance subject to the quantization effects. Sufficient conditions for the existence of the static output feedback strictly dissipative tracking controller are expressed in terms of linear matrix inequalities. Two simulation examples are provided to show the effectiveness of the developed design method.

Asynchronous dissipative filtering for nonlinear jumping systems subject to fading channels

Abstract: The fuzzy asynchronous dissipative filtering issue for Markov jump discrete-time nonlinear systems subject to fading channels is discussed in this paper, where the Rice fading model is employed to characterize the fading channels phenomenon in the system measurements for the first time. The attention is focused on developing an available asynchronous filter, which can ensure that the underlying error system is dissipative. In this regard, several important performances can be investigated conveniently by introducing adjustment matrices. By means of the stochastic analysis theory and the network control technique, some sufficient conditions for the solvability of the addressed problem are presented, simultaneously, the gains of the filter desired are determined correspondingly. An illustrative example is finally exploited to explain the utilizability of the developed approach.

Ultracold quantum wires with localized losses: Many-body quantum Zeno effect

Abstract: The effect of localized loss on a one-dimensional gas of interacting fermions is investigated. Here, the interplay of gapless quantum fluctuations and particle interactions strongly renormalizes the dissipative impurity. As a result, the loss probability for modes close to the Fermi energy vanishes for arbitrary strength of the dissipation, as a many-body incarnation of the quantum Zeno effect. This is reflected in the shape of the particle momentum distribution, exhibiting a peak close to the Fermi momentum.

Non-commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems.

Abstract: We study dynamical optimal transport metrics between density matrices associated to symmetric Dirichlet forms on finite-dimensional $$C^*$$ -algebras. Our setting covers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, and spectral gap estimates.

Warm brane inflation with an exponential potential: A consistent realization away from the swampland

Abstract: It has very recently been realized that coupling branes to higher dimensional quantum gravity theories and considering the consistency of what lives on the branes, one is able to understand whether such theories can belong either to the swampland or to the landscape. In this regard, in the present work, we study a warm inflation model embedded in the Randall-Sundrum brane-world scenario. It is explicitly shown that this model belongs to the landscape by supporting a strong dissipative regime with an inflaton steep exponential potential. The presence of extra dimension effects from the braneworld allow achieving this strong dissipative regime, which is shown to be both theoretically and observationally consistent. In fact, such strong dissipation effects, which decrease towards the end of inflation, together with the extra dimension effect, allow the present realization to simultaneously satisfy all previous restrictions imposed on such a model and to evade the recently proposed swampland conjectures. The present implementation of this model, in terms of an exponential potential for the scalar field, makes it also a possible candidate for describing the late-time Universe in the context of a dissipative quintessential inflation model, and we discuss this possibility in the Conclusions.

New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries

Abstract: We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we rev...