Coherent State Representation Research Articles

Fock space and field theoretic description of nonequilibrium work relations

Abstract We consider classical, interacting particles coupled to a thermal reservoir and subject to a local, time-varying potential while undergoing hops on a lattice. We impose detailed balance on the hopping rates and map the dynamics to the Fock space Doi representation, from which we derive the Jarzynski and Crooks relations. Here the local potential serves to drive the system far from equilibrium and to provide the work. Next, we utilize the coherent state representation to map the system to a Doi–Peliti field theory and take the continuum limit. We demonstrate that time reversal in this field theory takes the form of a gauge-like transformation which leaves the action invariant up to a generated work term. The time-reversal symmetry leads to a fundamental identity, from which we are able to derive the Jarzynski and Crooks relations, as well as a far-from-equilibrium generalization of the fluctuation-dissipation relation.

Phase-space representation of coherent states generated through SUSY QM for tilted anisotropic Dirac materials

In this paper, we examine the electron interaction within tilted anisotropic Dirac materials when subjected to external electric and magnetic fields possessing translational symmetry. Specifically, we focus on a distinct non-zero electric field magnitude, enabling the decoupling of the differential equation system inherent in the eigenvalue problem. Subsequently, employing supersymmetric quantum mechanics facilitates the determination of eigenstates and eigenvalues corresponding to the Hamiltonian operator. To delve into a semi-classical analysis of the system, we identify a set of coherent states. Finally, we assess the characteristics of these states using fidelity and the phase-space representation through the Wigner function.

Geometry transition in spinfoams

Abstract We show how the fixed-spin asymptotics of the EPRL model can be used to perform the spin-sum for spin foam amplitudes defined on fixed two-complexes without interior faces and contracted with coherent spin-network states peaked on a discrete simplicial geometry with macroscopic areas. We work in the representation given in Ref 1. We first rederive the latter in a different way suitable for our purposes. We then extend this representation to 2-complexes with a boundary and derive its relation to the coherent state representation. We give the measure providing the resolution of the identity for Thiemann's state in the twisted geometry parametrization. We then piece together these with other results in the literature and show how the spin sum can be performed analytically using the model asymptotics. These results are relevant to analytic investigations regarding the transition of a black hole to a white hole geometry. In particular, this work was the basis of the calculation presented in Ref 2.

Entanglement and Generalized Berry Geometrical Phases in Quantum Gravity

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum space–time. It is based on the Minimum Group Representation Principle (MGRP). Within this framework, new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space–times. Our main results here are as follows: (i) We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, such as the spectral scalar and tensor indices, nS and nT, and the tensor-to-scalar ratio r. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) Mp(n) representation for quantum de Sitter space–time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the Mp(n) group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) Mean value generators of Mp(2) are related to the adiabatic invariant and topological charge of the space–time, (matrix element of the transition −∞<t<∞). (v) The basic even and odd n-sectors of the Hilbert space are intrinsic to the quantum space–time and its discrete levels (in particular, continuum for n→∞), they do not require any extrinsic generation process such as the standard Schrodinger cat states, and are entangled. (vi) The gravity or cosmological on one side and another of the Planck scale are entangled. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity region and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space–time are entangled. (vii) The general classical-quantum gravity duality is associated with the Metaplectic Mp(n) group symmetry which provides the complete full covering of the phase space and of the quantum space–time mapped from it.

Quantum acoustics unravels Planckian resistivity

Strange metals exhibit universal linear-in-temperature resistivity described by a Planckian scattering rate, the origin of which remains elusive. By employing an approach inspired by quantum optics, we arrive at the coherent state representation of lattice vibrations: quantum acoustics. Utilizing this nonperturbative framework, we demonstrate that lattice vibrations could serve as active drivers in the Planckian resistivity phenomenon, challenging prevailing theories. By treating charge carriers as quantum wave packets negotiating the dynamic acoustic field, we find that a competition ensues between localization and delocalization giving rise to the previously conjectured universal quantum bound of diffusion, [Formula: see text], independent of temperature or any other material parameters. This leads to the enigmatic T-linear resistivity over hundreds of degrees, except at very low temperatures. Quantum diffusion also explains why strange metals have much higher electrical resistivity than typical metals. Our work elucidates the critical role of phonons in Planckian resistivity from a unique perspective and reconsiders their significance in the transport properties of strange metals.

Covariant operator bases for continuous variables

Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the basic observables, with the crucial property of behaving well under symplectic transformations. This basis is the analogue of the irreducible tensors widely used in the context of SU(2) symmetry. Given the density matrix of a state, the expansion coefficients in that basis constitute the multipoles, which describe the state in a canonically covariant form that is both concise and explicit. We use these quantities to assess properties such as quantumness or Gaussianity and to furnish direct connections between tomographic measurements and quasiprobability distribution reconstructions.

From Wigner hyperbolic rotation to fractional squeezing transformation

Based on the usual Wigner-Weyl transformation theory we find that the Wigner hyperbolic rotation in phase space will map onto fractional squeezing operator in Hilbert space. The merit of Weyl ordering and the coherent state representation of Fresnel operator is used in our derivation.

Phase space analysis of the 3-level Lipkin-Meshkov-Glick model using parity adapted U(D)-spin coherent states

We study the phase-space properties of the 3-level Lipkin-Meshkov-Glick as paradigmatic case of critical, parity symmetric, N-quDit systems undergoing a quantum phase transition in the thermodynamic limit N → ∞. We generalize U(2) spin coherent states to U(D) (quDits), and define the coherent state representation Qψ (Husimi function) of a symmetric N- quDit state |ψ〉 in the phase space ℂP D −1 = U(D)/[U(1) × U(D − 1)]. This allows us to define parity adapted U(D) coherent states (𝕔-DCATs), which reproduce accurately the lowest energy Hamiltonian eigenstates obtained by numerical diagonalization. We visualize precursors of the QPTs by plotting localization measures (Husimi function and its moments) of the parity adapted U(D) coherent states and the numerical Hamiltonian eigenstates for a finite number of particles.

Influence of NNN interaction and existence of breathers in a quasi-discrete Heisenberg helimagnetic spin system

In this work, we investigate the existence and properties of discrete bright and dark breathers in a one-dimensional Heisenberg helimagnet incorporating bilinear, helical, NNN and anisotropic interactions. The Hamiltonian is bosonized using the Dyson–Maleev transformation and the coherent state representation is selected as the fundamental representation of the system. With the help of multiple scales combined with quasi-discreteness approximation, the dynamical equation is reduced to a nonlinear Schrödinger equation (NLSE). By employing the solution of NLSE derived using inverse scattering technique (IST), the bright and dark type breather solutions are constructed. The effect of helicity and NNN interactions on these breather modes is also analysed.

Localization measures of parity adapted U(D)-spin coherent states applied to the phase space analysis of the D-level Lipkin-Meshkov-Glick model.

We study phase space properties of critical, parity symmetric, N-qudit systems undergoing a quantum phase transition (QPT) in the thermodynamic N→∞ limit. The D=3 level (qutrit) Lipkin-Meshkov-Glick model is eventually examined as a particular example. For this purpose, we consider U(D)-spin coherent states (DSCS), generalizing the standard D=2 atomic coherent states, to define the coherent state representation Q_{ψ} (Husimi function) of a symmetric N-qudit state |ψ〉 in the phase space CP^{D-1} (complex projective manifold). DSCS are good variational approximations to the ground state of an N-qudit system, especially in the N→∞ limit, where the discrete parity symmetry Z_{2}^{D-1} is spontaneously broken. For finite N, parity can be restored by projecting DSCS onto 2^{D-1} different parity invariant subspaces, which define generalized "Schrödinger cat states" reproducing quite faithfully low-lying Hamiltonian eigenstates obtained by numerical diagonalization. Precursors of the QPT are then visualized for finite N by plotting the Husimi function of these parity projected DSCS in phase space, together with their Husimi moments and Wehrl entropy, in the neighborhood of the critical points. These are good localization measures and markers of the QPT.

Deriving mixed state of light field by partial tracing pure state in higher dimension

In this paper, we show that by partial tracing the pure state in higher dimension one can deduce the mixed state of light field. In this paper the pure state in higher dimension is a three-mode squeezed state S23σS31τ000000S31−1τS23−1σ, while the mixed state’s density operator is sech2σsech2τea2†a3†tanhσsech2σtanh2τa3†a30220ea2a3tanhσ, which involves both squeezing and chaotic properties of optical field. We further explain how such kind of light field can be generated by passing a two-mode squeezed light though a single-mode dissipative channel, its Wigner function is discussed by using the coherent state representation. Our work provides an important method, which can be used to theoretically find more optical fields in quantum communication and quantum optics.

Quasi discreteness analysis of a two dimensional ferromagnetic spin system

By introducing bilinear and anisotropic interactions in a model based on a square lattice of ferromagnetism, we learn about the influence of excitations with nonlinearity in intrinsic localized modes (ILMS) and modulational instability. Equations of motion are constructed in the semi-classical limit by pairing Glauber’s coherent state representation with the Dyson-Maleev form of spin operators. A Cubic Nonlinear Schrödinger (CNLS) equation is obtained using an intensive method of quasi-discreteness analysis mixed with a method of multiple scales. We also analyze the bright envelope solitons and intrinsically localized modes using a Sine-Cosine function approach. Stability conditions are obtained using Modulational Instability analysis.

Transition from eigenmodes to geometric modes characterized by the quantum SU(2) coupled oscillator model: a review

The quantum and classical dynamics of the SU(2) coupled oscillator model are systematically reviewed to provide the quantum eigenstates and stationary coherent states for characterizing laser transverse modes from the analogy with the quantum-classical connection. The integral formula for the representation of the stationary coherent states derived from the evolution of the time-dependent wave packet state is completely reviewed. Several calculated results for the stationary coherent states are illustratively presented to display the spatial distributions for the quantum-classical transition and the plentiful variations of phase singularities. The overall review is believed to provide a comprehensive insight into laser transverse modes characterized by the stationary coherent states of the SU(2) coupled oscillator model.

Coherent state operators, giant gravitons, and gauge-gravity correspondence

We generalize a construction of coherent state operators describing various giant graviton branes. We enlarge the coherent state parameters, by including complementary coherent state parameters, to describe a system of dual giants and giants. One of the advantages of using complementary coherent state parameters is that they have rich sub-block structures that record different type of giant gravitons or wrapped branes. The coherent state parameters are further packaged into supermatrix, to construct new representations of coherent states, which encode information of both giants and dual giants. We add strings onto the coherent state operators. The string-added states capture near-BPS states. Hence the constructions of BPS coherent state operators are also useful for analyzing near-BPS states. The coherent state representations, auxiliary integrals, as well as auxiliary susy integrals, facilitate the computations efficiently. We describe multi-matrix operators and BPS states, and unify some classes of operators. Finally, reduced coherent states as well as their fermionic counterparts are discussed.

Coherent state representation of squeezing operator and its applications

In a previous paper Zhan et al. (2022) proposed the coherent state representation for linear operator, which shows a beautiful theoretical value. Inspired by the work, we further extend it to the nonlinear case, including single- and two-mode squeezing process. Based on squeezing operators’ transformation relation, we introduce their coherent state representations and derive their normal ordering forms by using the technique of integration within product of operator. As applications, we examine some operators’s normal ordering forms and show the entanglement property of prepared quantum states via the Schmidt decomposition. In particular, we further consider two cascaded two-mode squeezing operators, in which a generalized SU(1,1) interferometer is involved. In addition, the application of two-mode squeezing operator followed by photon-subtraction to generate non-Gaussian entangled states in quantum teleportation is discussed. Our results will be useful in preparation of quantum states and quantum metrology.

Coherent charge carrier dynamics in the presence of thermal lattice vibrations

We develop the coherent state representation of lattice vibrations to describe their interactions with charge carriers. In direct analogy to quantum optics, the coherent state representation leads from quantized lattice vibrations (phonons) naturally to a quasiclassical field limit, i.e., the deformation potential. To an electron, the deformation field is a sea of hills and valleys, as ``real'' as any external field, morphing and propagating at the sound speed, and growing in magnitude with temperature. In this disordered potential landscape, the charge carrier dynamics is treated nonperturbatively, preserving its coherence beyond single collision events. We show the coherent state picture agrees exactly with the conventional Fock state picture in perturbation theory. Furthermore, it goes beyond by revealing aspects that the conventional theory could not explain: transient localization even at high temperatures by charge carrier coherence effects, and band tails in the density of states due to the self-generated disorder (deformation) potential in a pure crystal. The coherent state paradigm of lattice vibrations supplies tools for probing important questions in condensed matter physics as in quantum optics.

Vibrational response functions for multidimensional electronic spectroscopy in the adiabatic regime: A coherent-state approach.

Multi-dimensional spectroscopy represents a particularly insightful tool for investigating the interplay of nuclear and electronic dynamics, which plays an important role in a number of photophysical processes and photochemical reactions. Here, we present a coherent state representation of the vibronic dynamics and of the resulting response functions for the widely used linearly displaced harmonic oscillator model. Analytical expressions are initially derived for the case of third-order response functions in an N-level system, with ground state initialization of the oscillator (zero-temperature limit). The results are then generalized to the case of Mth order response functions, with arbitrary M. The formal derivation is translated into a simple recipe, whereby the explicit analytical expressions of the response functions can be derived directly from the Feynman diagrams. We further generalize to the whole set of initial coherent states, which form an overcomplete basis. This allows one, in principle, to derive the dependence of the response functions on arbitrary initial states of the vibrational modes and is here applied to the case of thermal states. Finally, a non-Hermitian Hamiltonian approach is used to include in the above expressions the effect of vibrational relaxation.

Completeness of coherent state subsystems for nilpotent Lie groups

Let $G$ be a nilpotent Lie group and let $\pi$ be a coherent state representation of $G$. The interplay between the cyclicity of the restriction $\pi|_{\Gamma}$ to a lattice $\Gamma \leq G$ and the completeness of subsystems of coherent states based on a homogeneous $G$-space is considered. In particular, it is shown that necessary density conditions for Perelomov's completeness problem for the highest weight vector can be obtained via criteria for the cyclicity of $\pi|_{\Gamma}$.

Coherent state representation of thermal correlation functions with applications to rate theory.

A coherent state phase space representation of operators, based on the Husimi distribution, is used to derive an exact expression for the symmetrized version of thermal correlation functions. In addition to the time and temperature independent phase space representation of the two operators whose correlation function is of interest, the integrand includes a non-negative distribution function where only one imaginary time and one real time propagation are needed to compute it. The methodology is exemplified for the flux side correlation function used in rate theory. The coherent state representation necessitates the use of a smeared Gaussian flux operator whose coherent state phase space representation is identical to the classical flux expression. The resulting coherent state expression for the flux side correlation function has a number of advantages as compared to previous formulations. Since only one time propagation is needed, it is much easier to converge it with a semiclassical initial value representation. There is no need for forward-backward approximations, and in principle, the computation may be implemented on the fly. It also provides a route for analytic semiclassical approximations for the thermal rate, as exemplified by a computation of the transmission factor through symmetric and asymmetric Eckart barriers using a thawed Gaussian approximation for both imaginary and real time propagations. As a by-product, this example shows that one may obtain "good" tunneling rates using only above barrier classical trajectories even in the deep tunneling regime.

Nonlinear spin excitations in a Heisenberg antiferromagnet with NNN and D–M interactions

Spin deviation vs site number in an inhomogeneous (site dependent) antiferromagnet incorporating next nearest neighbour (NNN) and Dzyaloshinski–Moriya (D–M) interactions along with nearest neighbour and anisotropic interactions is investigated. In this context, a model Hamiltonian for 1D inhomogeneous antiferromagnetic spin system with site dependent inhomogenities is constructed. Glauber coherent state representation along with H-P representation is applied to derive the Heisenberg equation of motion. The dynamics in the continuum level is investigated using the Sine–Cosine (SC) function method and the results are analysed graphically.