Quasi-thermal State Research Articles

Characterizing the Non-equilibrium Dynamics of Field-Driven Correlated Quantum Systems

Recent experimental advances in ultrafast phenomena have triggered renewed interest in the dynamics of correlated quantum systems away from equilibrium. We review nonequilibrium dynamical mean-field theory studies of both the transient and the steady states of a DC field-driven correlated quantum system. In particular, we focus on the nonequilibrium behavior and how it relates to the fluctuation-dissipation theorem. The fluctuation-dissipation theorem emerges as an indicator for how the system thermalizes and for how it reaches a steady state. When the system thermalizes in an infinite temperature steady state it can pass through a succession of quasi-thermal states that approximately obey the fluctuation-dissipation theorem. We also discuss the Wigner distribution and what its evolution tells us about the nonequilibrium many-body problem.

Quasithermalization of collisionless particles in quadrupole potentials

We analyze several puzzling features of a recent experiment with a noninteracting gas of atoms in a quadrupole trap. After an initial momentum kick, the system reaches a stationary, quasi-thermal state even without collisions, due to the dephasing of individual particle trajectories. Surprisingly, the momentum distribution remains anisotropic at long times, characterized by different "temperatures" along the different directions. In particular, there is no transfer of the kick energy between the axial and radial trap directions. To understand these effects we discuss and solve two closely related models: a spherically symmetric trap $V(r)\simeq r^\alpha$ and a strongly confined gas along one direction (a "pancake" trap). We find that in the isotropic trap, the gas unexpectedly also preserves the anisotropy of the kick at long times, which we are able to explain using the conservation of angular momentum and the virial theorem. Depending on the value of $\alpha$ we find that the kick can cool or heat the orthogonal directions. The pancake trap case is quantitatively similar to the quadrupole one. We show that for the former, the temperature anisotropy and memory of the kick direction are due to the change in the 2D effective potential resulting from the kick, thereby also explaining the quadrupole experimental results.

Cosmological perturbations in the entangled inflationary universe

In this paper it is presented the model of a multiverse made up of universes which are created in entangled pairs that conserve the total momentum conjugated to the scale factor. For the background spacetime it is assumed a FRW metric with a scalar field with mass $m$ minimally coupled to gravity. For the fields that propagate in the entangled spacetimes it is considered the perturbations of the spacetime and the scalar field, whose quantum states become entangled too. They turn out to be in a quasi thermal state and the corresponding thermodynamical magnitudes are computed. Three observables are expected to be caused by the creation of the universes in entangled pairs: a modification of the Friedmann equation because the entanglement of the spacetimes, a modification of the effective value of the potential of the scalar field by the backreaction of the perturbation modes, and a modification of the spectrum of fluctuations because the thermal distribution induced by the entanglement of the partner universes. The later would be a distinctive feature of the creation of universes in entangled pairs.

Topological order of mixed states in correlated quantum many-body systems

Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order. Here we discuss possible extensions of this concept to density matrices describing statistical ensembles. For a large class of quasi-thermal states, which can be realized as thermal states of some quasi-local Hamiltonian, we generalize earlier definitions of density matrix topology to generic many-body systems with strong correlations. We point out that the robustness of topological order, defined as a pattern of long-range entanglement, depends crucially on the perturbations under consideration. While it is intrinsically protected against local perturbations of arbitrary strength in an infinite closed quantum system, purely local perturbations can destroy topological order in open systems coupled to baths if the coupling is sufficiently strong. We discuss our classification scheme using the finite-temperature quantum Hall states and point out that the classical Hall effect can be understood as a finite temperature topological phase.

Monodromies and functional determinants in the conformal field theory driven quantum cosmology

We apply the monodromy method for the calculation of the functional determinant of a special second order differential operator $F=-d^2/d\tau^2+{\ddot g}/g$, $\ddot g= d^2g/d\tau^2$, subject to periodic boundary conditions with a periodic zero mode $g=g(\tau)$. This operator arises in applications of the early Universe theory and, in particular, determines the one-loop statistical sum for the microcanonical ensemble in cosmology generated by a conformal field theory (CFT). This ensemble realizes the concept of cosmological initial conditions by generalizing the notion of the no-boundary wavefunction of the Universe to the level of a special quasi-thermal state which is dominated by instantons with an oscillating scale factor of their Euclidean Friedmann-Robertson-Walker metric. These oscillations result in the multi-node nature of the zero mode $g(\tau)$ of $F$, which is gauged out from its reduced functional determinant by the method of the Faddeev-Popov gauge fixing procedure. The calculation is done for a general case of multiple nodes (roots) within the period range of the Euclidean time $\tau$, thus generalizing the previously known result for the single-node case of one oscillation of the cosmological scale factor. The functional determinant of $F$ expresses in terms of the monodromy of its basis function, which is obtained in quadratures as a sum of contributions of time segments connecting neighboring pairs of the zero mode roots within the period range.

Wigner Functions and Tomograms of the Even and Odd Negative Binomial States

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, the Wigner functions of the even and odd negative binomial states (NBSs) are obtained. We concentrate our analysis on the fact that the even and odd NBSs interpolate between the even and odd coherent states and the even and odd quasi-thermal states depending on the values of the parameters involved. Moreover, the tomograms of the even and odd NBSs are calculated by virtue of intermediate coordinate-momentum representation in quantum optics.

Cosmological landscape and Euclidean quantum gravity

Quantum creation of the universe is described by the density matrix defined by the Euclidean path integral. This yields an ensemble of universes—a cosmological landscape—in a mixed quasi-thermal state which is shown to be dynamically more preferable than the pure quantum state of the Hartle–Hawking type. The latter is suppressed by the infinitely large positive action of its instanton, generated by the conformal anomaly of quantum matter. The Hartle–Hawking instantons can be regarded as posing initial conditions for Starobinsky solutions of the anomaly driven de Sitter expansion, which are thus dynamically eliminated by infrared effects of quantum gravity. The resulting landscape of hot universes treated within the cosmological bootstrap (the self-consistent back reaction of quantum matter) turns out to be limited to a bounded range of the cosmological constant, which rules out a well-known infrared catastrophe of the vanishing cosmological constant and suggests an ultimate solution to the problem of unboundedness of the cosmological action in Euclidean quantum gravity.

Algebraic structure and nonclassical properties of the negative hypergeometric state

A new class of the intermediate state of the quantized radiation field, i.e. the negative hypergeometric state (NHGS), is introduced and its algebraic structure and nonclassical properties are investigated. The importance of NHGS lies in the fact that it can help unify such important states as the binomial, negative binomial, coherent, number and quasi-thermal states etc in quantum optics.

Some statistical properties of the even and the odd negative binomial states

New states of electromagnetic field, i.e. even and odd negative binomial states are introduced here. These states interpolate between the even (odd) coherent states and the even (odd) quasi-thermal states. Various statistical properties of these states such as the mean photon number, second-order coherence function, normal squeezing are calculated. The Wigner function for these states are also discussed. These results may be useful for carrying out systematic study of the non-classical properties of `Schrodinger cat states' as one moves from even (odd) coherent state to even (odd) quasi-thermal state.