Annals of Physics最新文献

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.

We use the Hilbert space formulation of classical mechanics, known as the Koopman–von Neumann formalism, to study adiabatic driving, geometric phases, and the geometric tensor for classical states. In close relation to what happens to a quantum state, a classical Koopman–von Neumann eigenstate will acquire a geometric phase factor $exp\left(i\Phi \right)$ after a closed variation of the parameters $\lambda$ in its associated Hamiltonian. The explicit form of $\Phi$ is then derived for integrable systems, and its relation with the Hannay angle is shown. Additionally, we use quantum formulas to write an adiabatic gauge potential that generates adiabatic unitary flow between classical eigenstates, and we explicitly show the relationship between the potential and the classical geometric phase. We also define a classical analog of the geometric tensor, thus defining a Fubini–Study metric for classical states, and we use the singularities of the tensor to link the transition from Arnold–Liouville integrability to chaos with some of the mathematical formalism of quantum phase transitions. While the formulas and definitions we use originate in quantum mechanics, all the results found are purely classical, no classical or semiclassical limit is ever taken.

Ladder operators are useful, if not essential, in the analysis of some given physical system since they can be used to find easily eigenvalues and eigenvectors of its Hamiltonian. In this paper we extend our previous results on abstract ladder operators considering in many details what happens if the Hamiltonian of the system is not self-adjoint. Among other results, we give an existence criterion for coherent states constructed as eigenstates of our lowering operators. In the second part of the paper we discuss two different examples of our framework: pseudo-quons and a deformed generalized Heisenberg algebra. Incidentally, and interestingly enough, we show that pseudo-quons can be used to diagonalize an oscillator-like Hamiltonian written in terms of (non self-adjoint) position and momentum operators which obey a deformed commutation rule of the kind often considered in minimal length quantum mechanics.

This paper presents the effects of non-minimal Lorentz-violation operators in superconductivity. By constructing a Lorentz-Violating Ginzburg–Landau theory of superconductivity with a five-dimensional operator, we discuss the influence of higher dimensional Lorentz-Violating operators in the London’s depth penetration, in the coherence length and critical magnetic field.

This study seeks a better comprehension of anomalies by exploring $(n+1)$-point perturbative amplitudes in a $2n$-dimensional framework. The involved structures combine axial and vector vertices into odd tensors. This configuration enables diverse expressions, considered identities at the integrand level. However, connecting them is not automatic after loop integration, as the divergent nature of amplitudes links to surface terms. The background to this subject is the conflict between the linearity of integration and the translational invariance observed in the context of anomalies. That prohibits the simultaneous satisfaction of all symmetry and linearity properties, constraints that arise through Ward identities and relations among Green functions. Using the method known as Implicit Regularization, we show that trace choices are a means to select the amount of anomaly contributions appearing in each symmetry relation. Such an idea appeared through recipes to take traces in recent works, but we introduce a more complete view. We also emphasize low-energy theorems of finite amplitudes as the source of these violations, proving that the total amount of anomaly remains fixed regardless of any choices.