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At least 1,567 records · Page 87
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DOE OSTI2019

A covariant simultaneous action for branes

Highlights: • A novel variational approach is presented. • It provides a shortcut towards the second variation of geometrical models. • This should be of interest, for its generality, to various areas of theoretical physics. - Abstract: A covariant simultaneous action for branes in an arbitrary curved background spacetime is considered. The term ‘simultaneous’ is imported from variational calculus and refers to the fact that extremization of the action produces at once both the first and second variations of a given geometrical action for the brane. The action depends on a pair of independent field variables, the brane embedding functions, through the canonical momentum of a reparametrization invariant geometric model for the brane, and an auxiliary vector field. The form of the action is analogous to a symplectic potential. Extremization of the simultaneous action produces at once the equations of motion and the Jacobi equations for the brane geometric model, and it also provides a convenient shortcut towards its second variation. In this note, we consider geometric models depending only on the intrinsic geometry of the brane worldvolume, and discuss briefly the generalization to extrinsic geometry dependent models. The approach is illustrated for Dirac–Nambu–Goto [DNG] branes. For a relativistic particle, a simultaneous action was introduced by Ba z-dot ański, that served as an inspiration for the present work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Phase space quantum–classical hybrid model

Highlights: •Semiclassical model including back-action reaction beyond mean-field approximation. •Quantum–classical hybridization holds for all times as well as all intensities. •Wigner–Weyl phase-space correspondence mixing quantum with classical systems. -- Abstract: In this work we provide a complete model of semiclassical theories by including back-reaction and correlation into the picture. We specially aim at the interaction between light and a two-level atom, and we also illustrate it via the coupling of two harmonic oscillators. Quantum and classical systems are treated on the same grounds via the Wigner–Weyl phase-space correspondence of the quantum theory. We show that this model provides a suitable mixture of the quantum and classical degrees of freedom, including the fact that the evolution transfers nonclassical features to the classical subsystem and nonquantum behaviour to the quantum subsystem. In that sense, we can no longer distinguish between classical and quantum variables and we need to talk about a hybrid model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Exact solution of the relativistic Dunkl oscillator in (2+1) dimensions

In this paper we study the (2+1)-dimensional Dirac–Dunkl oscillator coupled to an external magnetic field. Our Hamiltonian is obtained from the standard Dirac oscillator coupled to an external magnetic field by changing the partial derivatives by the Dunkl derivatives. We solve the Dunkl–Klein–Gordon-type equations in polar coordinates in a closed form. The angular part eigenfunctions are given in terms of the Jacobi–Dunkl polynomials and the radial functions in terms of the Laguerre functions. Also, we compute the energy spectrum of this problem and show that, in the non-relativistic limit, it properly reduces to the Hamiltonian of the two dimensional harmonic oscillator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

The exact discontinuity of a partial wave along the left-hand cut and the exact N∕D method in non-relativistic scattering

We first deduce the analytical continuation in the complex planes of the initial and final three-momenta of the Lippmann–Schwinger equation in coupled or uncoupled partial-wave amplitudes. This result allows us to deduce a master equation whose solution is the exact discontinuity of the on-shell partial-wave amplitudes along the left-hand cut. This equation is always a linear non-singular integral equation whose solution is fixed exclusively by the knowledge of the potential, applicable to either regular or singular potentials. The capability of calculating exactly this discontinuity allows one to settle the exact N∕D method in two-body non-relativistic scattering for coupled and uncoupled waves. We exemplify this new advance in scattering theory by explicitly checking the agreement between the Lippmann–Schwinger equation with the corresponding solutions of the exact N∕D method for some examples that involve regular and singular potentials, either attractive or repulsive.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Diagonal entropy and topological phase transitions in extended Kitaev chains

We investigate the diagonal entropy for ground states of the extended Kitaev chains with extensive pairing and hopping terms. The systems contain rich topological phases equivalently represented by topological invariant winding numbers and Majorana zero modes. Both the finite size scaling law and block scaling law of the diagonal entropy are studied, which indicates that the diagonal entropy demonstrates volume effect. The parameter of volume term is regarded as the diagonal entropy density, which can identify the critical points of symmetry-protected topological phase transitions efficiently in the studied models, even for those with higher winding numbers. The formulation of block scaling law and the capability of diagonal entropy density in detecting topological phase transitions are independent of the chosen bases. In order to manifest the advantage of diagonal entropy, we also calculate the global entanglement, which cannot show clear signatures of the topological phase transitions. This work provides a new quantum-informatic approach to characterize the feature of the topologically ordered states and may motivate a deep understanding of the quantum coherence and diagonal entropy in various condensed matter systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Gravastars in (3+1) dimensions admitting Karmarkar condition

Highlights: • Model of Gravastar in (3+1) dimensions is studied under GR. • Karmarkar condition of Embedding class 1 has been incorporated. • The class 1 condition provides an exact solution of three regions of gravastar. • Surface redshift confirms the stability of the model which is non-singular. - Abstract: The development of gravastar model by Mazur and Mottola (2004) is one of the most acceptable alternatives of conventional classical black hole. They have studied phase transition of the collapsing stellar objects at low temperature near event horizon which leads to the condensate phase, i.e. Bose–Einstein condensation. In the present study we have obtained a unique solution of this gravastar model under Einstein’s GR in (3+1) dimensions by incorporating the Karmarkar condition for embedding class 1. The most important motive of this work is to find an exact solution of the shell without taking the thin shell approximation. We have obtained singularity free finite solutions for the interior of the gravastar.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Causal hydrodynamic fluctuations in non-static and inhomogeneous backgrounds

Highlights: •The fluctuation–dissipation relation is modified by inhomogeneous backgrounds. •The constitutive equations are restricted by causality and fluctuation properties. •The structure of constitutive equation gives a natural cutoff scale of the theory. •The memory function with tensor structures in inhomogeneous backgrounds is obtained. -- Abstract: To integrate hydrodynamic fluctuations, namely thermal fluctuations of hydrodynamics, into dynamical models of high-energy nuclear collisions based on relativistic hydrodynamics, the property of the hydrodynamic fluctuations given by the fluctuation–dissipation relation should be carefully investigated. The fluctuation–dissipation relation for causal dissipative hydrodynamics with the finite relaxation time is naturally given in the integral form of the constitutive equation by the linear-response theory. While, the differential form of the constitutive equation is commonly used in analytic investigations and dynamical calculations for practical reasons. We give the fluctuation–dissipation relation for the general linear-response differential form and discuss the restrictions to the structure of the differential form, which comes from the causality and the positive semi-definiteness of the noise autocorrelation, and also the relation of those restrictions to the cutoff scale of the hydrodynamic fluctuations. We also give the fluctuation–dissipation relation for the integral form in non-static and inhomogeneous background by introducing new tensors, the pathline projectors. We find new modification terms to the fluctuation–dissipation relation for the differential form in non-static and inhomogeneous background which are particularly important in dynamical models to describe rapidly expanding systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Superintegrable systems from block separation of variables and unified derivation of their quadratic algebras

Highlights: • A new method for constructing D-dimensional minimally superintegrable systems. • Superintegrable systems from block coordinate separation of variables. • Unified derivation of quadratic symmetry algebras via gauge transformations. - Abstract: We present a new method for constructing D-dimensional minimally superintegrable systems based on block coordinate separation of variables. We give two new families of superintegrable systems with N (N≤D) singular terms of the partitioned coordinates and involving arbitrary functions. These Hamiltonians generalize the singular oscillator and Coulomb systems. We derive their exact energy spectra via separation of variables. We also obtain the quadratic algebras satisfied by the integrals of motion of these models. We show how the quadratic symmetry algebras can be constructed by novel application of the gauge transformations from those of the non-partitioned cases. We demonstrate that these quadratic algebraic structures display a universal nature to the extent that their forms are independent of the functions in the singular potentials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Degenerate Hamiltonian operator in higher-order canonical gravity — The problem and a remedy

Different routes towards canonical formulation of a classical theory result in different canonically equivalent Hamiltonians, while their quantum counterparts are related through appropriate unitary transformation. However, for higher-order theory of gravity although two Hamiltonians emerging from the same action differing by total derivative terms are related through canonical transformation, the difference transpires while attempting canonical quantization, which is predominant in non-minimally coupled higher-order theory of gravity. We follow Dirac’s constraint analysis to formulate phase-space structures, in the presence (case-I) and absence (case-II) of total derivative terms. While the coupling parameter plays no significant role as such for case-I, quantization depends on its form explicitly in case-II, and as a result unitary transformation relating the two is not unique. We also find certain mathematical inconsistencies in case-I, for modified Gauss–Bonnet-Dilatonic coupled action, in particular. Thus, we conclude that total derivative terms indeed play a major role in the quantum domain and should be taken care of a-priori, for consistency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

DC conductivity from backreacted non-linear arcsin electrodynamics

Highlights: • This model, reproduces conductivity and Hall angle of high-T{sub c} cuprates. • It exhibits metal-insulator transition under variation of magnetic field. • Obtained transport properties for a backreacted non-linear electrodynamics model. - Abstract: We consider arcsin electrodynamics in a holographic set up along with dilatonic and axionic scalar fields. Considering backreaction of the matter fields on the geometry we study direct conductivity of the dual theory and obtain the conductivity matrix. Since obtaining an exact solution is difficult in general, we have studied several limiting cases. In particular, at the strong momentum dissipation limit, we find for hyperscaling violating geometry as the background, the resistivity and Hall coefficient will behave as ∼T and ∼T{sup 2} respectively. Then we restrict to a simpler model, where we find that the variation of the magnetic field can lead to metal–insulator transition/crossover.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

New results on asymmetric thick branes

This work deals with the presence and stability of thick brane solutions in the warped five dimensional braneworld scenario with a single extra spatial dimension of infinite extent. We combine two distinct procedures that give rise to new possibilities, allowing that we describe models of asymmetric thick branes, with the asymmetry being controlled by a single real parameter. We illustrate the main results with some distinct models, which show that the method works for both standard and generalized models, and the solutions are gravitationally stable against small perturbations of the metric.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Solving scattering problems in the half-line using methods developed for scattering in the full line

We reduce the solution of the scattering problem defined on the half-line [0,∞) by a real or complex potential v(x) and a general homogeneous boundary condition at x=0 to that of the extension of v(x) to the full line that vanishes for x<0. We find an explicit expression for the reflection amplitude of the former problem in terms of the reflection and transmission amplitudes of the latter. We obtain a set of conditions on these amplitudes under which the potential in the half-line develops bound states, spectral singularities, and time-reversed spectral singularities where the potential acts as a perfect absorber. We examine the application of these results in the study of the scattering properties of a δ-function potential and a finite barrier potential defined in [0,∞), discuss optical systems modeled by these potentials, and explore the configurations in which these systems act as a laser or perfect absorber. In particular, we derive an explicit formula for the laser threshold condition for a slab laser with a single mirror and establish the surprising fact that a nearly perfect mirror gives rise to a lower threshold gain than a perfect mirror. We also offer a nonlinear extension of our approach which allows for utilizing a recently developed nonlinear transfer matrix method in the full line to deal with finite-range nonlinear scattering interactions defined in the half-line.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Exact solution of the A{sub 2}{sup (2)} model with non-diagonal boundary reflections

The exact solution of the A{sub 2}{sup (2)} model (or the Izergin–Korepin model) with non-diagonal boundary reflections of the type I is studied by using the off-diagonal Bethe ansatz method. The complete operator product identities of the transfer matrices are obtained with the help of fusion. Based on them and the asymptotic behaviors as well as the values at special points, the inhomogeneous T−Q relations of the system are constructed. The method and the results in this paper can be generalized to the high rank A{sub n}{sup (2)} case directly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Entanglement estimation in non-optimal qubit states

Highlights: • Quantum Fisher Information. • Entanglement Estimation. • Squeezed States. • Husimi Function. - Abstract: In the last years, a relationship has been established between the quantum Fisher information (QFI) and quantum entanglement. In the case of two-qubit systems, all pure entangled states can be made useful for sub-shot-noise interferometry while their QFI meets a necessary and sufficient condition (Hyllus et al., 2010). In M-qubit systems, the QFI provides just a sufficient condition in the task of detecting the degree of entanglement of a generic state (Pezzé and Smerzi, 2009). In our work, we show analytically that, for a large class of one-parameter non-optimal two-qubit states, the maximally entangled states are associated with stationary points of the QFI, as a function of such parameter. We show, via numerical simulations, that this scenario is maintained for the generalisation of this class of states to a generic M-qubit system. Furthermore, we suggest a scheme for an interferometer able to detect the entanglement in a large class of two-spin states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Time-evolution methods for matrix-product states

Highlights: • Introductory review of time-evolution methods for matrix-product states. • Detailed description of five state-of-the-art algorithms. • Extended comparison of numerical examples. • Extended error analysis of each algorithm. • Pseudo-code examples towards an implementation where necessary. - Abstract: Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO W{sup I,II} method, the global Krylov method, the local Krylov method and the one- and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Canonical scalar field inflation with a Woods–Saxon potential

This paper focuses on the realization of an inflationary model from a canonical scalar field theory with a Woods–Saxon potential, in the slow-roll approximation. Our analysis indicates that the observable quantities derived theoretically from our model, namely the spectral index of the primordial scalar curvature perturbations and the tensor-to-scalar ratio, are compatible with the latest Planck collaboration data. We also discuss the qualitative features of the potential, and we show that the value of the scalar field for which the graceful exit occurs, coincides with the inflection point of the scalar potential. We also attempt to study the post-inflation reheating phase of the model, in order to further examine the viability of the Woods–Saxon scalar field model, and as we demonstrate the results indicate viability of the model for this era too, however the instantaneous reheating is not allowed for the model at hand.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Comment on “The Mössbauer rotor experiment and the general theory of relativity” [Ann. Physics 368 (2016) 258–266]

Highlights: •Our approach is considered from the viewpoint of arbitrary moving continuum. •Continuum characteristics are determined by a deformation tensor, a stress tensor, a strain velocity tensor, a spin tensor (Sing (1963)) and the first curvature vectors of the world lines of medium particles. •All these physical values are located on the hypersurfaces orthogonal to the world lines of medium particles and specify the “physical” space. •The time counting from the “physical” space permits to obtain the red shift of the frequency at the end of the tube that coincides with Corda result (Corda (2016)).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms

Lie–Trotter–Suzuki decompositions are an efficient way to approximate operator exponentials exp ( t H ) when H is a sum of n (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution algorithms for tensor network states, digital quantum simulation protocols, path integral methods like quantum Monte Carlo, and splitting methods for symplectic integrators in classical Hamiltonian systems. Here, we provide optimized decompositions up to order t 6 . The leading error term is expanded in nested commutators (Hall bases) and we minimize the 1-norm of the coefficients. For n = 2 terms, several of the optima we find are close to those in McLachlan (1995). Generally, our results substantially improve over unoptimized decompositions by Forest, Ruth, Yoshida, and Suzuki. We explain why these decompositions are sufficient to efficiently simulate any one- or two-dimensional lattice model with finite-range interactions. This follows by solving a partitioning problem for the interaction graph.

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