Unitarity and Page Curve for Evaporation of 2D AdS Black Holes

We explore the Hawking evaporation of two-dimensional anti-de Sitter (AdS2), dilatonic black hole coupled with conformal matter, and derive the Page curve for the entanglement entropy of radiation. We first work in a semiclassical approximation with backreaction. We show that the end-point of the evaporation process is AdS2 with a vanishing dilaton, i.e., a regular, singularity-free, zero-entropy state. We explicitly compute the entanglement entropies of the black hole and the radiation as functions of the horizon radius, using the conformal field theory (CFT) dual to AdS2 gravity. We use a simplified toy model, in which evaporation is described by the forming and growing of a negative mass configuration in the positive-mass black hole interior. This is similar to the “islands” proposal, recently put forward to explain the Page curve for evaporating black holes. The resulting Page curve for AdS2 black holes is in agreement with unitary evolution. The entanglement entropy of the radiation initially grows, closely following a thermal behavior, reaches a maximum at half-way of the evaporation process, and then goes down to zero, following the Bekenstein–Hawking entropy of the black hole. Consistency of our simplified model requires a non-trivial identification of the central charge of the CFT describing AdS2 gravity with the number of species of fields describing Hawking radiation.

Polaron Models with Regular Interactions at Strong Coupling

We study a class of polaron-type Hamiltonians with sufficiently regular form factor in the interaction term. We investigate the strong-coupling limit of the model, and prove suitable bounds on the ground state energy as a function of the total momentum of the system. These bounds agree with the semiclassical approximation to leading order. The latter corresponds here to the situation when the particle undergoes harmonic motion in a potential well whose frequency is determined by the corresponding Pekar functional. We show that for all such models the effective mass diverges in the strong coupling limit, in all spatial dimensions. Moreover, for the case when the phonon dispersion relation grows at least linearly with momentum, the bounds result in an asymptotic formula for the effective mass quotient, a quantity generalizing the usual notion of the effective mass. This asymptotic form agrees with the semiclassical Landau–Pekar formula and can be regarded as the first rigorous confirmation, in a slightly weaker sense than usually considered, of the validity of the semiclassical formula for the effective mass.

Comparative Analysis of Standard ΛCDM and ΛCS Models

We draw a comparison of time-dependent cosmological parameters calculated in the standard ΛCDM model with those of the model of a homogeneous and isotropic Universe with non-zero cosmological constant filled with a perfect gas of low-velocity cosmic strings (ΛCS model). It is shown that pressure-free matter can obtain the properties of a gas of low-velocity cosmic strings in the epoch, when the global geometry and the total amount of matter in the Universe as a whole obey an additional constraint. This constraint follows from the quantum geometrodynamical approach in the semiclassical approximation. In terms of general relativity, its effective contribution to the field equations can be linked to the time evolution of the equation of state of matter caused by the processes of redistribution of the energy between matter components. In the present article, the exact solutions of the Einstein equations for the ΛCS model are found. It is demonstrated that this model is equivalent to the open de Sitter model. After the scale transformation of the time variable of the ΛCS model, the standard ΛCDM and ΛCS models provide the equivalent descriptions of cosmological parameters as functions of time at equal values of the cosmological constant. The exception is the behavior of the deceleration parameter in the early Universe.

Canonical equivalence, quantization and inflation for higher-order theory of gravity

Canonical formulation of higher-order theory of gravity has been attempted over decades. Different routes lead to different phase-space structures of the Hamiltonian. Although, these Hamiltonians are canonically equivalent at the classical level, their quantum counterparts may not be same, due to nonlinearity. Earlier, it has been proved that ‘Dirac constraint analysis’ (after taking care of divergent terms) and ‘Modified Horowitz’ Formalism’ lead to identical phase-space structure of the Hamiltonian for the gravitational action with scalar curvature squared terms. For the sake of completeness, this paper expatiates the extension of the same work for a general fourth-order gravitational action. Canonical quantization and semiclassical approximation are performed to explore that such a quantum theory transits successfully to a classical de-Sitter Universe. Inflation is also studied. Inflationary parameters show excellent agreement with the recently released Planck’s data.

Semiclassical Qubits

The semiclassical approximation of quantum computing and quasi-qubits (s-bits) have been obtained by us as a result of our work over the past few years. This work can be conventionally divided into two parts. The first part, let’s call it the programming model, contains a computer model of quasi-qubits and quantum computing. The second part, let’s call it the microelectronic model, describes the microelectronic realization of qubits in the semiclassical approximation (quasi-qubits) and exists in the form of block diagrams, which are supposed to be easy to manufacture. How did we get the semiclassical approximation? The difficulty in solving such a problem was that microparticles in quantum mechanics are described in an infinite-dimensional Hilbert space. Classical models are much poorer in the number of variables; therefore, it is impossible to describe quantum mechanical objects by classical methods due to the small number of available parameters.

Semiclassical approximation meets Keldysh–Schwinger diagrammatic technique: scalar $$\varphi ^4$$

We study the evolution of the non-equilibrium quantum fields from a highly excited initial state in two approaches: the standard Keldysh–Schwinger diagram technique and the semiclassical expansion. We demonstrate explicitly that these two approaches coincide if the coupling constant g and the Plank constant $$\hbar $$ ħ are simultaneously small. Also, we discuss loop diagrams of the perturbative approach, which are summed up by the leading order term of the semiclassical expansion. As an example, we consider shear viscosity for the scalar field theory at the leading semiclassical order. We introduce the new technique that unifies both semiclassical and diagrammatic approaches and open the possibility to perform the resummation of the semiclassical contributions.

Semiclassical approach for excitonic spectrum of Coulomb coupling between two Dirac particles

The properties of the energy spectrum of excitons in monolayer transition metal dichalcogenides are investigated using a multiband model. In the multiband model, we use the excitonic Hamiltonian in the product base of the Dirac single-particle states at the conduction and valence band edges. Following the separation of variables, we decouple the corresponding energy eigenvalue system of the first-order ODE radial equations rigorously and solve the resulting second-order ODE self-consistently, using the finite difference method, thus we determine the energy eigenvalues of the discrete excitonic spectrum and the corresponding wave functions. We also developed a WKB approach to solve the same spectral problem in semiclassical approximation for the resulting ODE. We compare the results for the energy spectrum and the corresponding eigen-function forms for WS 2 and WSe 2 obtained by means of both methods. We also compare our results for the energy spectrum with other theoretical works for excitons, and with available experimental data.

Quantum Implications of Non-Extensive Statistics

Exploring the analogy between quantum mechanics and statistical mechanics, we formulate an integrated version of the Quantropy functional. With this prescription, we compute the propagator associated to Boltzmann–Gibbs statistics in the semiclassical approximation as K=F(T)exp(iScl/ℏ). We determine also propagators associated to different nonadditive statistics; those are the entropies depending only on the probability S± and Tsallis entropy Sq. For S±, we obtain a power series solution for the probability vs. the energy, which can be analytically continued to the complex plane and employed to obtain the propagators. Our work is motivated by the work of Nobre et al. where a modified q-Schrödinger equation is obtained that provides the wave function for the free particle as a q-exponential. The modified q-propagator obtained with our method leads to the same q-wave function for that case. The procedure presented in this work allows to calculate q-wave functions in problems with interactions determining nonlinear quantum implications of nonadditive statistics. In a similar manner, the corresponding generalized wave functions associated to S± can also be constructed. The corrections to the original propagator are explicitly determined in the case of a free particle and the harmonic oscillator for which the semiclassical approximation is exact, and also the case of a particle with an infinite potential barrier is discussed.

Плотность энергетического спектра электрона в поле изображения и запирающем электрическом поле

In the semiclassical approximation, the density of the electron energy spectrum near the metal surface is described, when electron is bound by the image field and the blocking electrostatic field. In the system under consideration, the confinement mechanism is realized, and the energy spectrum for the motion of an electron in the direction perpendicular to the metal surface is completely discrete. The density of states of the energy spectrum is expressed in terms of elliptic integrals, the argument of which is a sigmoidal function. When the field is turned off, it becomes the Heaviside step function. A dimensionless energy parameter is introduced, which determines the intervals with qualitatively different changes in the width of the classically accessible region of motion. For large positive values of the energy parameter, the spectrum density asymptotically tends to the density in the triangular potential with the addition of the Coulomb logarithmic correction, and for negative values of the energy parameter, the spectrum density tends to dependence for a one-dimensional Coulomb potential. Approximate expressions are obtained for the spectrum density in terms of elementary functions in a wide range of electron energies and electric field strength.

Расчет ядерных тормозных способностей в квазиклассическом приближении

The results of calculating nuclear stopping in the semiclassical approximation for the systems H-Be, H-C, H-W, O-C, O-Be, O-Al are presented. It was found that in the presence of a well in the interatomic interaction potential, an additional maximum appears in the dependence of the nuclear stopping on the energy of the bombarding particles. When using the universal potential without a well, this feature is absent. It is shown that by scaling the data obtained for systems with hydrogen are recalculated for collisions with the participation of hydrogen isotopes D and T. The results obtained are in good agreement with classical calculations, which is explained by the fact that large scattering angles make the main contribution to the nuclear stopping, and the applicability criterion changes to the condition: angular momentum ℓ >> 1.