Annals of Physics最新文献

$p$-Adic quantum mechanics is constructed from the Dirac–von Neumann axioms identifying quantum states with square-integrable functions on the $N$-dimensional $p$-adic space, $Q_p^N$. This choice is equivalent to the hypothesis of the discreteness of the space. The time is assumed to be a real variable. The $p$-adic quantum mechanics is motivated by the question: what happens with the standard quantum mechanics if the space has a discrete nature? The time evolution of a quantum state is controlled by a nonlocal Schrödinger equation obtained from a $p$-adic heat equation by a temporal Wick rotation. This $p$-adic heat equation describes a particle performing a random motion in $Q_p^N$. The Hamiltonian is a nonlocal operator; thus, the Schrödinger equation describes the evolution of a quantum state under nonlocal interactions. In this framework, the Schrödinger equation admits complex-valued plane wave solutions, which we interpret as $p$-adic de Broglie waves. These mathematical waves have all wavelength $p^{-1}$. In the $p$-adic framework, the double-slit experiment cannot be explained using the interference of the de Broglie waves. The wavefunctions can be represented as convergent series in the de Broglie waves, but the $p$-adic de Broglie waves are just mathematical objects. Only the square of the modulus of a wave function has a physical meaning as a time-dependent probability density. These probability densities exhibit interference patterns similar to the ones produced by ‘quantum waves’. In the $p$-adic framework, in the double-slit experiment, each particle goes through one slit only. The $p$-adic quantum mechanics is an analog (or model) of the standard one under the hypothesis of the existence of a Planck length. The precise connection between these two theories is an open problem. Finally, we propose the conjecture that the classical de Broglie wave-particle duality is a manifestation of the discreteness of space–time.

Thermodynamically stable low-temperature phases of the Bose–Fermi mixtures composed of bosons and spinless fermions close to four dimensions are considered. In the regime, where the only boson–fermion two-body interaction is present and tuned to unitary limit, the properties of a system solely depend on the mass and number ratios of constituent atoms. In addition to the phase with the dimers (boson–fermion shallow bound states), we identified one more state of the mixture with the coexistence of fermionic dimers and trimers. The universal physics of these phases, whose characteristic feature is an absence of the Bose–Einstein condensate, is discussed.

The analysis of empirical data through model-free inequalities leads to the conclusion that violations of Bell-type inequalities by empirical data cannot have any significance unless one believes that the universe operates according to the rules of a mathematical model.

The quantum theory of black holes has opened up a window to study the intersection of general relativity and quantum field theory, but perceived paradoxes concerning the fate of classical information directed at a black hole horizon, as well as concerning the unitarity of the evaporation process, have led researchers to question the very foundations of physics. In this pedagogical review I clarify the ramifications of the fact that black holes not only emit radiation spontaneously, but also respond to infalling matter and radiation by emitting approximate clones of those fields in a stimulated manner. I review early purely statistical arguments based on Einstein’s treatment of black bodies, and then show that the Holevo capacity of the black hole (the capacity to transmit classical information through a quantum channel) is always positive. I then show how stimulated emission turns the black hole into an almost optimal quantum cloning machine, and furthermore discuss the capacity of black holes to transmit quantum information. Taking advantage of an analogy between black hole physics and non-linear optics I show that a calculation of the evolution of a black hole over time, using a discretization of the black hole $S$-matrix path integral, yields well-behaved Page curves suggesting that black hole evaporation is unitary. Finally, I speculate about possible observable consequences of stimulated emission of radiation in black holes.

The electronic transport properties of two junctions (BGB, GBG) made of borophene (B) and graphene (G) are investigated. Using the transfer matrix method with Chebyshev polynomials, we have studied single and multiple barriers in a superlattice configuration. We showed that a single barrier exhibits remarkable tilted transport properties, with perfect transmission observed for both junctions under normal incidence. We found that robust superlattice transmission is maintained for multiple barriers, particularly in the BGB junction. It turns out that by varying the incident energy, many gaps appear in the transmission probability. The number, width, and position of these transmission gaps can be manipulated by adjusting the number of cells, incident angle, and barrier characteristics. For diffuse transport, we observed considerable variations in transmission probability, conductance and the Fano factor, highlighting the sensitivity of these junctions to the physical parameters. We showed different behaviors between BGB and GBG junctions, particularly with respect to the response of conductance and Fano factor when barrier height varies. For ballistic transport, we have seen that the minimum scaled conductance is related to the maximum Fano factor, demonstrating their control under specific conditions of the physical parameters. Analysis of the length ratio (geometric factor) revealed some remarkable patterns, where scaled conductance and the Fano factor converged to certain values as the ratio approached infinity.

The theory of Self-Consistent Green’s Function (SCGF) is reformulated in an explicit Nambu-covariant fashion for applications to many-body systems at non-zero temperature in symmetry-broken phases. This is achieved by extending the Nambu-covariant formulation of perturbation theory, presented in the first part of this work, to non-perturbative schemes based on self-consistently dressed propagators and vertices. We work out in detail the self-consistent ladder approximation, motivated by a trade-off between numerical complexity and many-body phenomenology. Taking a complex general Hartree–Fock–Bogoliubov (HFB) propagator as a starting point, we also formulate and prove a sufficient condition on the stability of the HFB self-energy to ensure the convergence of the initial series of ladders at any energy. The self-consistent ladder approximation is written purely in terms of spectral functions and the resulting set of equations, when expressed in terms of Nambu tensors, are remarkably similar to those in the symmetry-conserving case. This puts the application of the self-consistent ladder approximation to symmetry-broken phases of infinite nuclear matter within reach.

In this work, we propose an alternative path to establish a gauge theory for magnetic monopoles. The approach involves a simple improvement of the original formulation by Dirac and is based on utilizing non-global potentials associated with Dirac strings. In the present case, we adopt the concept of generalized vector fields to build up generalized gauge potentials for the electromagnetic fields. The main advantage is to work with just one single global (generalized) vector potential to describe the monopole field throughout the entire space, except at the point where the monopole is located, rather than adopting multi-valued functions. We argue that the treatment presented in this paper also leads to electric charge quantization, similar to the case with the Dirac monopoles. We discuss the point-like source associated with the monopole we hope it could be helpful for the search of magnetic monopoles in the laboratory.

This paper presents a nonperturbative method for solving eigenproblems. This method applies to almost all potentials and provides nonperturbative approximations for any energy level. The method converts an eigenproblem into a perturbation problem, obtains perturbation solutions through standard perturbation theory, and then analytically continues the perturbative solution into a nonperturbative solution. Concretely, we follow three main steps: (1) Introduce an auxiliary potential that can be solved exactly and treat the potential to be solved as a perturbation on this auxiliary system. (2) Use perturbation theory to obtain an approximate polynomial of the eigenproblem. (3) Use a rational approximation to analytically continue this approximate polynomial into the nonperturbative region.

In this paper we address the relation between the star exponentials emerging within the Deformation Quantization formalism and Feynman’s path integrals associated with propagators in quantum dynamics. In order to obtain such a relation, we start by visualizing the quantum propagator as an integral transform of the star exponential by means of the symbol corresponding to the time evolution operator and, thus, we introduce Feynman’s path integral representation of the propagator as a sum over all the classical histories. The star exponential thus constructed has the advantage that it does not depend on the convergence of formal series, as commonly understood within the context of Deformation Quantization. We include some basic examples to illustrate our findings, recovering standard results reported in the literature. Further, for an arbitrary finite dimensional system, we use the star exponential introduced here in order to find a particular representation of the star product which may be recognized as the one encountered in the context of the quantum field theory for a Poisson sigma model.

Symmetry-breaking considerations play an important role in allowing reliable and accurate predictions of complex systems in quantum many-body simulations. The general theory of perturbations in symmetry-breaking phases is nonetheless intrinsically more involved than in the unbroken phase due to non-vanishing anomalous Green’s functions or anomalous quasiparticle interactions. In the present paper, we develop a formulation of many-body theory at non-zero temperature which is explicitly covariant with respect to a group containing Bogoliubov transformations. Based on the concept of Nambu tensors, we derive a factorisation of standard Feynman diagrams that is valid for a general Hamiltonian. The resulting factorised amplitudes are indexed over the set of un-oriented Feynman diagrams with fully antisymmetric vertices. We argue that, within this framework, the design of symmetry-breaking many-body approximations is simplified.