Statistical Quasiparticles Research Articles

Dissipatons as generalized Brownian particles for open quantum systems: Dissipaton-embedded quantum master equation.

Dissipaton theory had been proposed as an exact, nonperturbative approach to deal with open quantum system dynamics, where the influence of the Gaussian environment is characterized by statistical quasi-particles, named dissipatons. In this work, we revisit the dissipaton equation of motion theory and establish an equivalent dissipaton-embedded quantum master equation (DQME) that gives rise to dissipatons as generalized Brownian particles. As explained in this work, the DQME supplies a direct approach to investigate the statistical characteristics of dissipatons and, thus, the physically supporting hybrid bath modes. Numerical demonstrations are carried out on the electron transfer model, exhibiting the transient statistical properties of the solvation coordinate.

A statistical quasi-particles thermofield theory with Gaussian environments: System-bath entanglement theorem for nonequilibrium correlation functions.

For open quantum systems, the Gaussian environmental dissipative effect can be represented by statistical quasi-particles, namely, dissipatons. We exploit this fact to establish the dissipaton thermofield theory. The resulting generalized Langevin dynamics of absorptive and emissive thermofield operators are effectively noise-resolved. The system-bath entanglement theorem is then readily followed between an important class of nonequilibrium steady-state correlation functions. All these relations are validated numerically. A simple corollary is the transport current expression, which exactly recovers the result obtained from the nonequilibrium Green's function formalism.

Zero-temperature limit and statistical quasiparticles in many-body perturbation theory

The order-by-order renormalization of the self-consistent mean-field potential in many-body perturbation theory for normal Fermi systems is investigated in detail. Building on previous work mainly by Balian and de Dominicis, as a key result we derive a thermodynamic perturbation series that manifests the consistency of the adiabatic zero-temperature formalism with perturbative statistical mechanics---for both isotropic and anisotropic systems---and satisfies at each order and for all temperatures the thermodynamic relations associated with Fermiliquid theory. These properties are proved to all orders.

Dissipaton equation of motion for system-and-bath interference dynamics

In this review we give a comprehensive account on the dissipaton equation of motion (DEOM) approach to quantum mechanics of open systems. This approach provides a statistical quasi-particle (dissipaton) picture for the environment, as it participates in the correlated system-and-bath dynamics. The underlying dissipaton algebra is de facto established via a close comparison with the celebrated hierarchical equations of motion formalism that is rooted at the Feynman-Vernon influence functional path integral formalism. As a quasi-particle generalization, DEOM identifies unambiguously the physical meanings of all involving dynamical variables as many-dissipaton configurations. It addresses the dynamics of not only systems but also hybridizing bath degrees of freedom. We demonstrate these features of DEOM via its real-time evaluation of the Fano interference of an analytically solvable model system, with the highlight that the statistical quasi-particle picture is ubiquitous, implied even in those commonly used quantum master equations.

Spin dynamics in spin-polarized Fermi systems

We present a simple description of transverse dynamics of dilute Fermi systems in terms of statistical quasiparticles. We give explicit expressions for the quasiparticle interaction function and collision integral at arbitrary temperatures, and discuss the implications of this approach in classical and degenerate regions, including the quantum gases. The results provide an unexpected explanation for the zero-temperature attenuation in transverse spin dynamics and peculiar I2-terms in molecular field as imaginary (pole) and real (principal) parts of the quasiparticle interaction function.

Statistical quasiparticles in transverse dynamics of gases.

We analyze the validity of the Fermi-liquid approach to transverse dynamics of spin-polarized gases at arbitrary temperatures. We demonstrate that the diagrammatic kinetic equation for transverse processes can be formulated as a simpler, but completely equivalent equation in terms of quasiparticles. The equation includes all coherent and dephasing molecular-6eld terms as well as the dissipative collision integral up to the second order. Beyond the second order, the results become very complicated, and a quasiparticle approach loses its attraction. We give the expressions for the efFective interaction function and collision integral for statistical quasiparticles, applicable at all temperatures, and discuss the implications of this concept at high temperatures. The interaction function contains anomalous pole terms which do not exist in equations for longitudinal dynamics. This provides a somewhat unexpected interpretation for zero-temperature dissipative processes, observed recently in spin dynamics, and for controversial molecular-field terms (the so-called I2 terms) as imaginary (pole) and real (principal) parts of the quasiparticle interaction function. These molecular-6eld terms with complicated analytical structure do not vanish completely, as was assumed earlier, in the Boltzmann region, but contribute to higher-order density terms. With an emphasis on quantum gases, we discuss how to reconcile various physical assumptions inherent to different kinetic approaches to dilute gases.

Quasiparticle spectra and the calculation of thermodynamics for a two-dimensional Fermi liquid.

If the dynamical quasiparticle spectrum of a Fermi liquid (FL), ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{dy}}$, given by the poles of the single-particle propagator, is used in the expression for the entropy of a noninteracting Fermi gas, one finds that the result is different from that calculated directly from the thermodynamic potential. In particular, the coefficient of the ${\mathit{T}}^{3}$lnT terms, the leading correction to the linear T dependence for a three-dimensional (3D) FL, is overestimated when calculated from ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{dy}}$. The thermodynamic properties may be calculated correctly from a second quasiparticle spectrum, the statistical quasiparticle spectrum, ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}^{\mathrm{st}}$. In this paper I calculate the corrections to leading linear energy and temperature dependences for a 2D FL. I compare the difference between the two spectra in the 2D and 3D cases. Although these differences are qualitatively the same, they are quantitatively larger in the 2D case.

Diagonalization of propagators in thermo field dynamics for relativistic quantum fields

Two-point functions for interacting quantum fields in statistical systems can be diagonalized by matrix transformations. It is shown, that within the framework of time-dependent Thermo Field Dynamics this diagonalization can be understood as a thermal Bogoliubov transformation to non-interacting statistical quasi-particles. The condition for their unperturbed propagation relates these states to the thermodynamic properties of the system: It requires global equilibrium for stationary situations, or specifies the time evolution according to a kinetic equation.

Diagonalization of full finite temperature Green's functions by quasi-particles

For thermal systems, standard perturbation theory breaks down because of the absence of stable, observable asymptotic states. We show, how the introduction of statistical quasi-particles (stable, but not observable) gives rise to a consistent description. Statistical and spectral information can be cleanly separated also for interacting systems.

Statistical quasi-particles as the normal component of a superfluid

It is argued from the structure of many body theory Feynman graphs that the statistical average of a spontaneously broken conserved charge density decomposes naturally into two parts: (1) a “normal” part given by an ideal gas-like expression with statistical quasi-particle emergies, and (2) a “superfluid” part which vanishes when the symmetry is restored. The momentum density of a relativistic superfluid is also discussed.

Quasiparticle spectra and specific heat of a normal Fermi liquid in a spin-fluctuation model.

We calculate statistical and dynamical quasiparticle energies of a normal Fermi liquid in a spin-fluctuation model. The properties of spin fluctuations in the model are the same as those given by Landau Fermi-liquid theory at long wavelengths, low frequencies, and low temperatures if all Landau parameters except ${F}_{0}^{a}$ are neglected. The statistical quasiparticle spectrum is found to be significantly less dependent on momentum and temperature than the dynamical quasiparticle one. The specific heat is calculated both from the statistical quasiparticle spectrum and from the thermodynamic potential, and for parameters appropriate for liquid $^{3}\mathrm{He}$, the corrections to the leading low-temperature result (\ensuremath{\propto}T) are well characterized by ${T}^{3}$lnT behavior up to temperatures of order 100 mK, which is in qualitative agreement with what Greywall finds experimentally. If the Landau parameter ${F}_{1}^{a}$ is included in the calculation in addition to ${F}_{0}^{a}$, we find rather good agreement between theory and experiment. A further conclusion of our work is that the finite-temperature contributions to the specific heat are much less sensitive to variations of the cutoff momentum in our calculations than is the spin-fluctuation contribution to the effective mass. Spin fluctuations are therefore able to account for finite-temperature effects, even though they provide only a modest contribution to the effective mass. We also investigate the reason for earlier calculations in the paramagnon model giving very low estimates of the temperature below which the specific heat should exhibit ${T}^{3}$lnT behavior, and find that this is due to (i) the fact that the dynamical quasiparticle contribution to the specific heat was calculated and (ii) the use of the paramagnon model, rather than Landau theory.

Magnetic susceptibility of submonolayer3He films

We calculate the magnetic susceptibility of submonolayer3He films. First, using the formulation of the equilibrium thermodynamic properties in terms of statistical quasiparticles, we obtain an expression for the magnetic susceptibility of dilute systems of particles interacting through a short-range potential, taking into account binary interactions between the particles. At high temperatures our expression reduces to the one obtained using the virial expansion truncated after the second term. Next, we apply this expression to3He in two dimensions and compare our results with the magnetic susceptibility data of submonolayer3He films adsorbed on Grafoil and on argon-coated Grafoil and previous calculations.

Elementary particle scattering and statistical quasi-particles in quantum statistical mechanics

Previous work relating the thermodynamic potential to elementary particle S-matrix elements is generalized and rederived directly from the expressions for the diagrams of many body theory. The divergent physical region poles are shown to introduce energy derivatives of mass shell delta functions which tend to shift the energies of the scattering particles away from the elementary particle mass shell. These shifted energies are related to the statistical quasiparticle energies introduced by Balian and De Dominicis. The work of these authors is generalized to show that to all orders in the coupling strengths the many body diagrams for any system described by a relativistic or non-relativistic field theory can be summed to give: (1) the entropy and the statistical average of a non-spontaneously broken, conserved charge in terms of ideal gas-like formulae involving statistical quasi-particle energies; (2) the thermodynamic potential in terms of diagonal matrix elements of products of transition amplitudes wherein the energies of all external particles and the energy arguments of all ideal gas occupation numbers are the statistical quasi-particle energies.

Elementary particle scattering and statistical quasi-particles in quantum statistical mechanics: Richard E. Norton. Department of Physics, University of California, Los Angeles, California

When biased at a voltage just below a superconductor's energy gap, a tunnel junction between this superconductor and a normal metal cools the latter. While the study of such devices has long been focused to structures of submicron size and consequently cooling power in the picowatt range, we have led a thorough study of devices with a large cooling power up to the nanowatt range. Here we describe how their performance can be optimized by using a quasi-particle drain and tuning the cooling junctions' tunnel barrier.Polarisée à une tension juste inférieure à la bande interdite du supraconducteur, une jonction tunnel entre ce supraconducteur et un métal normal peut refroidir ce dernier. Alors que les études de ces dispositifs se sont longtemps concentrées sur des structures de taille submicronique, en conséquence avec des puissances de refroidissement de l'ordre du picowatt, nous avons mené une étude complète de jonctions NIS avec une forte puissance de refroidissement, de l'ordre du nanowatt. Dans cette revue, nous décrivons comment leurs performances peuvent être optimisées par l'ajout d'un drain pour les quasi-particles et l'ajustement de la barrière tunnel des jonctions réfrigérantes.

Statistical quasi-particles and the thermodynamics of hot dense matter

Abstract A single-particle description of a relativistic fluid, such as the quark-gluon plasma, is formulated as an extension of the Landau theory of Fermi liquids. By requiring consistency with conservation laws and irreversible thermodynamics, a transport theory appropriate to the hydrodynamic regime is set up. Expressions for the thermodynamic densities and the irreversible flows are found in terms of the quasi-particle spectral function and interaction function. The former is the first, and the latter the second variation of the grand potential with respect to the one-particle distribution functions. A recently proposed thermodynamic model for the quark-hadron phase transition is discussed in this context.

Effective electron mass in finite temperature QED

A quasi-particle description of a quantum electrodynamical plasma at finite temperature and density is sought in the context of the imaginary-time formalism of quantum field theory. Functional techniques and analytic continuation are used to derive an expression for the charge density, of the same form as valid for a non-interacting system, in terms of an effective propagator similar to, but different from, the conventional many-body fermion propagator. In contrast to the latter, the effective propagator possesses a pole on the real axis. This defines a statistical quasi-particle, in the sense of Balian and de Dominicis, having a real mass, which is explicitly evaluated at the one-loop level. Remarkable features of this lowest-order mass are that it is independent of the chemical potential, and that it implies a zero-temperature mass shift.

Diagrammatic Approach to the Anderson Model for Dilute Alloys

Applications of a new diagrammatic technique for the grand partition function Z and the susceptibility of the Anderson Hamiltonian are presented, where the hopping is treated as a perturbation. Z is expressed quite generally in terms of statistical quasiparticles. For -εd>W (bandwidth) and for U→∞ for simplicity, this formulation allows one to show that the thermodynamics of the Anderson model and of an s-d model with an effective J (essentially in agreement, but slightly renormalized compared to the one obtained from the Schrieffer-Wolff transformation) are equivalent. Indication is given that this equivalence is more complicated for the dynamical properties of the model, as reflected, e.g., by the scattering matrix.

Statistical quasiparticles, effective green's functions, and Landau descriptions of quantum liquids I. Impurity Systems at Equilibrium

This paper deals with Landau descriptions of quantum liquids, which are exact, in the sense that their derivation appeals to no approximation, and relies only on the convergence of the expansions involved. An extension of the validity of Landau's results is obtained, together with diagrammatic expansions for Landau's parameters. In this first part, we restrict to noninteracting particles in a random external field describing impurities. The impurities are distributed either homogeneously or at lattice sites. Such a system, though not a Landau-Fermi liquid in the usual sense, retains several features of the general system of interacting fermions. The method used is straightforward, the only delicate point being raised by the need for a regularization procedure whenever integrands with vanishing denominators show up. The final result expresses thermodynamic observables in terms of an effective Green's function G k eff( y), defined on the real axis. G k eff has a single real pole at y = ε k with a real residue Z k , and describes a “statistical quasiparticle”. The energy ε k replaces here the complex pole of the causal Green's function usually associated with elementary excitations and bears a simple relation with the single-particle level density. The Gibbs potential itself turns out to be exactly the same as for noninteracting particles of energies ε k . Alternatively, it may be obtained as the stationary value of a functional of the statistical quasiparticle energies ε k (in a way reminiscent of Brillouin-Wigner expansions), of the wavefunction renormalization constants Z k , and of the quasiparticle occupation numbers F k . The validity of this formulation is tested by a study of the convergence of a typical subseries. Self-contained appendices are devoted to a discussion of the general regularization problem and to the extension of Lagrange expansions to matrices, respectively.