Annals of Physics最新文献

A method is described for the extrapolation of perturbative expansions in powers of asymptotically small coupling parameters or other variables onto the region of finite variables and even to the variables tending to infinity. The method involves the combination of ideas from renormalization group theory, approximation theory, dynamical theory, and optimal control theory. The extrapolation is realized by means of self-similar factor approximants, whose control parameters can be uniquely defined. The method allows to find the large-variable behavior of sought functions knowing only their small-variable expansions. Convergence and accuracy of the method are illustrated by explicit examples, including the so-called zero-dimensional field theory and anharmonic oscillator. Strong-coupling behavior of Gell-Mann–Low functions in multicomponent field theory, quantum electrodynamics, and quantum chromodynamics is found, being based on their weak-coupling perturbative expansions.

We study the Uhlmann geometric phase of a spin-1 particle subjected to zero-field splitting (ZFS) interaction, modulated by a dimensionless parameter $\alpha$, under the effect of an external magnetic field with a tilting angle $\theta$. We show that the ZFS term induces a transition in the geometrical phase behavior, characterized by a critical parameter value, $\alpha ={\alpha }_c$. For $\alpha <{\alpha }_c$, this phase displays two critical temperatures at $\theta =\pi /2$, similar to spin-1 systems without ZFS, but with a separation that varies with $\alpha$. In contrast, for $\alpha >{\alpha }_c$, the phase exhibits two singularities at a single critical temperature but at different field orientations $\theta \ne \pi /2$. The phase disappears for significantly large $\left|\alpha \right|$, regardless of the values of the Hamiltonian parameters. This behavior clearly departs from the usual thermal Uhlmann phase observed in SU(2) systems. In addition, we analytically calculate the heat capacity, which, for $\theta =\pi /2$ and nearby values, displays two different regimes according to the sign of $\alpha$. For $\alpha <0$, it develops two peaks associated to the multilevel nature of the system, while for $\alpha >0$ only a single Schottky-anomaly like peak appears as in two level systems. Interestingly, when $\theta =\pi /2$, the temperature centroids of the Uhlmann phase and the heat capacity coincide in the region between critical temperatures for a given value of $\alpha <{\alpha }_c$. Furthermore, we demonstrate that when $\alpha =0$, the Uhlmann phase, a global topological property of the system, can be expressed as a function of the thermal component of the Bures metric, a local geometric property related to the heat capacity.

We consider inflation with a constant rate of rolling in which a complex scalar field plays the role of inflaton during the inflationary epoch. We implement the inflationary analysis for an accredited angular speed $\dot{\theta }$ which satisfies our dynamical equations. Scalar and tensorial perturbations generated in the framework of constant roll inflation with a complex field are studied. In this respect, we find analytically solutions to the gauge invariant fluctuations, with which an expression for the scalar power spectrum together with its scalar index spectral in this scenario were found. By comparing the obtained results with the observations coming from the cosmic microwave background anisotropies, the constraints on the parameters space of the model and also its predictions are analyzed and discussed.

We establish a new family of hairy black hole solutions of quartic quasi-topological gravity sourced by logarithmic electrodynamics and conformal scalar field. Here, we derive the metric function defining black hole structures and investigate the effects of electric charge, scalar hair, and dimensionality parameters on the location of the event horizon. The corresponding hairy black hole solution of the quartic quasi-topological gravity sourced by Maxwell field is also deduced in this setup. In addition, we also compute thermodynamic quantities for these objects such as temperature, entropy and heat capacity, and check the first law of thermodynamics. Furthermore, the impacts of scalar hair and electric charge on the divergences of heat capacity and extreme black hole’s horizon radius are also investigated. Finally, we also analyze thermodynamic stability and critical behavior of the resultant hairy black holes at the event horizon.

We compute the Galois group of a polynomial whose roots are determined by the critical points of a scalar potential in type IIB compactifications. We focus our study on certain perturbative models where it is feasible to construct a de Sitter vacuum within the effective theory by introducing non-geometric fluxes, D-branes or non-BPS states. Our findings clearly show that all de Sitter vacua derived from lifting AdS stable vacua are associated with an unsolvable Galois group. This suggests a deeper connection between the fundamental principles of Galois theory and its applications in the construction of dS vacua.

We describe a quantum particle constrained on a catenoid, employing an effective description of quantum mechanics based on expected values of observables and quantum dispersions. We obtain semiclassical trajectories for particles, displaying general features of the quantum behavior; most interestingly, particles present tunneling through the throat of the catenoid, a characteristic having important physical applications.

It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics, respectively. These schemes are based on an unusual feature, a formal redoubling of the degrees of freedom. Several arguments to motivate the redoubling are put forward in classical and quantum mechanics to demonstrate that such a formalism is natural.

The electric potential and the electromagnetic field for a linearly accelerated Born–Infeld charged particle are obtained in an inertial frame by a method that can, in principle, be applied to any electromagnetic theory. The method is based on (i) the fact that the metric near the horizon of a Schwarzschild black hole is equivalent to that of Rindler spacetime, and (ii) a theorem that guarantees that the electrostatic potential for a given nonlinear theory in a static, spherically symmetric spacetime is entirely specified by the Maxwellian electrostatic potential in the same background. Using analytical and numerical methods, the features of the radiation field and the radiation-reaction for such an accelerated particle are discussed in detail.

We investigate the one-dimensional tetramerised Kitaev chain induced by imaginary potentials $\{i\gamma ,-i\gamma ,-i\gamma ,i\gamma \}$ applied to the dimerised Kitaev chain. It is found that the imaginary potentials cause a variety of topological phase transitions. When the chemical potential $\mu$ is tuned to the energy zero point, they lead to the appearance of the mixed phase of the system consisting of two purely real Kitaev-like modes and four purely imaginary energy SSH-like zero-energy modes, which appear as the transition of the Kitaev-like-mixed-SSH-like phase. In addition, the Kitaev-like phase can be broadened by imaginary potentials, manifested as the widening of the quantised Andreev reflection plateau. When $\mu \ne 0$, the same topological phase transition occurs, from the topologically-trivial phase to the Kitaev-like phase. One can believe that this work provides theoretical support for probing the generation of Majorana zero modes in new topological superconducting systems.

We present a nonperturbative theory of bound states in the continuum (BICs) based on the analytical theory of infinite-grating eigenmodes in the case of a planar grating waveguide, that is, 1D photonic crystal slab. We describe a mixed BIC mainly formed by a coherent mixture of two photonic-crystal normal modes in a vicinity of their avoided crossing where both of them have a nonzero coupling with a radiation-loss channel. We reveal the universal properties of the mixed BIC associated with the spatial parity symmetry breaking and self-similar spectral behavior of the bulk normal modes near $\Gamma$-point. We show that the mechanism of the mixed-BIC formation constitutes a special kind of the generic Friedrich–Wintgen mechanism. A cutoff from the radiation-loss channel and extremely high-Q narrow resonance are achieved due to the destructive interference of the two crossing normal modes. On the contrary, a conventional symmetry-protected BIC is formed mostly by a single photonic-crystal normal mode which has vanishing coupling Fourier coefficient with every available radiation-loss channel. Implementation of the mixed BICs in various photonic-crystals structures could lead to interesting applications.