Annals of Physics最新文献

We propose a protocol based on a tunneling plus particle-detection process aimed at generating tripartite entanglement in a system of 3 indistinguishable fermions in a triple-well potential, initially prepared in a state exhibiting only exchange correlations. Particular attention is paid to the generation of fermionic ghz- and w-type states, which are analogous to the usual ghz- and w-type states defined in composites of distinguishable qubits. The protocol succeeds in generating fermionic w-type states, and the ensuing state becomes effectively equivalent to a 3-distinguishable-qubit w-type state shared among three localized parties. The protocol, however, is unable to generate ghz-type states, a result that highlights the fundamental inequivalence between these two types of states, and throws light into the characterization of processes that guarantee the emergence of specific kinds of multipartite entanglement in systems of identical parties. Our findings suggest new paths for the exploration, generation and exploitation of multipartite entanglement in composites of indistinguishable particles, as a useful resource for quantum information processing.

Ever since Hawking highlighted the puzzle of the existence of a singularity in the classical spacetime of general relativity, implying breakdown of all laws of physics living in the classical spacetime, singularity resolution became a problem of significantly high importance. This undesirable feature, indicating loss of predictability, has intrigued physicists over several decades. It has been hoped that the classical singularity would be resolved in a quantum theory of gravity. However, no appropriate wave function in the vicinity of the black hole singularity has been obtained so far to reach a definite conclusion.

In this paper, we focus upon the interior of the Schwarzschild black hole, plagued by a non-removable classical singularity. We consider the interior spacetime of the black hole to be represented by the Kantowski–Sachs metric. Since in a quantum mechanical scenario, existence of spontaneous fluctuations of matter fields should not be ignored, we include a Klein–Gordon field in the system. Quantizing this simple gravity-matter model in the canonical scheme, we obtain the Wheeler–DeWitt equation and find an exact solution in the minisuperspace variables.

We find that there exist three classes of solutions belonging to three different subregions of the eigenvalue space. Two of these classes of solutions admit the DeWitt criterion, a necessary condition for singularity resolution, implied by vanishing of the wave function at the singularity. These solutions are well-behaved and finite in the vicinity of the singularity and they indicate the existence of regular black holes in quantum gravity. In these classes of solutions, we further find that the expectation value of the Kretschmann operator is well-behaved and regular near the singularity, confirming a definite resolution to the puzzle of classical black hole singularity. On the other hand, there exists a small subregion in the eigenvalue space where the solution does not satisfy both conditions, the DeWitt criterion and finiteness of the Kretschmann expectation value at the singularity. This last class of solutions does not represent regular quantum black holes.

A gauge invariant mathematical formalism based on deformation quantization is outlined to model an $N=2$ supersymmetric system of a spin $1/2$ charged particle placed in a nocommutative plane under the influence of a vertical uniform magnetic field. The noncommutative involutive algebra $(C^{\infty }\left(R^2\right)\left[\left[\vartheta \right]\right],{\ast }^r)$ of formal power series in $\vartheta$ with coefficients in the commutative ring $C^{\infty }\left(R^2\right)$ was employed to construct the relevant observables, viz., SUSY Hamiltonian $H$, supercharge operator $Q$ and its adjoint $Q^{†}$ all belonging to the 2 × 2 matrix algebra $M_2(C^{\infty }\left(R^2\right)\left[\left[\vartheta \right]\right],{\ast }^r)$ with the help of a family of gauge-equivalent star products ${\ast }^r$. The energy eigenvalues of the SUSY Hamiltonian all turned out to be independent of not only the gauge parameter $r$ but also the noncommutativity parameter $\vartheta$. The nontrivial Fermionic ground state was subsequently computed associated with the zero energy which indicates that supersymmetry remains unbroken in all orders of $\vartheta$. The Witten index for the noncommutative SUSY Landau problem turns out to be $-1$ corroborating the fact that there is no broken supersymmetry for the model we are considering.

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.