arXiv subjects

M. C. Baldiotti

Publications and source records attributed to M. C. Baldiotti.

At least 19 recordsLinked to original sources

arXiv2026

Quasi-local Hamiltonian for generalized Kerr-Schild black holes in the Iyer-Wald formalism

Grounded in the covariant phase space approach of the Iyer-Wald formalism, we propose a quasi-local Hamiltonian for generalized Kerr-Schild (GKS) black holes. Evaluated for spherically symmetric spacetimes over a flat Minkowski background, our formulation recovers the Misner-Sharp mass. Because this framework relies solely on the GKS structure, it provides a straightforward extension of the Misner-Sharp mass to rotating geometries. We further extend our analysis to asymptotically anti-de Sitter (AdS) black holes, where a renormalization procedure to subtract the background AdS energy naturally emerges. By employing this technique, we establish a geometric quasi-local formulation of Kerr-AdS thermodynamics.

gr-qc↗

arXiv2026

Scaling Symmetry in Symplectic Thermodynamics

This paper investigates scaling symmetry in thermodynamics by unifying constrained Hamiltonian dynamics with symplectic and contact geometries. Through the mathematical processes of contactization and symplectization, we demonstrate that fixing an extended global scale variable effectively recovers the standard thermodynamic description in terms of scale-invariant quantities. The geometric formalism is illustrated by establishing the diffeomorphism between the Lagrangian submanifolds of ideal and van der Waals gases. Finally, applying this framework to a Schwarzschild black hole reveals that breaking the scale symmetry between internal energy and entropy is a fundamental physical requirement to accommodate non-isothermal dynamics.

math-ph↗

arXiv2026

Quantum-statistical constraints on Kerr-anti-de Sitter thermodynamics

We develop a general framework for interpreting the thermodynamic descriptions of Kerr-anti de Sitter black holes (KadS). These descriptions satisfy a first law and respect the homogeneity required by scaling properties. Additionally, they are subject to restrictions from semiclassical arguments. We show that temperature and angular velocity are kinematic quantities tied to a reference frame, identified through the Euclidean formalism. However, the pressure-volume contribution is a dynamical term that requires a gauge fixing of the potential mass and volume. It is established that the observer associated with a given thermodynamic description is directly encoded in the Killing vector that generates the horizon. We demonstrate that the quantum statistical relation restricts the infinite family of KadS descriptions to a subclass that reduces to Schwarzschild-adS and Kerr thermodynamics in the limits of vanishing cosmological constant and angular momentum. Furthermore, we establish the uniqueness of both the description associated with a frame co-rotating with infinity, and the description whose thermodynamic and geometric volumes coincide. Thus, our framework provides a coherent interpretation of the variety of KadS thermodynamics, reconciling geometric and quantum-statistical considerations.

gr-qc↗

arXiv2024

Generating Kerr-anti-de Sitter thermodynamics

In the present work we study the construction of different thermodynamic descriptions for the Kerr-anti-de Sitter (KadS) black holes. The early versions of the KadS thermodynamics are briefly discussed, highlighting some of its strong points and shortcomings. Isohomogeneous transformations, a procedure for generating new thermodynamics, are presented and geometrically interpreted for KadS. This tool is used to determine possible KadS thermodynamics that can be constructed to satisfy a Smarr formula, and the validity of the first law in the generated thermodynamics. The connection between new thermodynamic theories and early Hawking's approach is considered. In this new framework, the usual KadS thermodynamics is complemented with its geometric construction, and Hawking's proposal, which does not satisfy the first law, is improved to an alternative thermodynamic theory. With the quantum statistical relation, Hawking's and this alternative KadS thermodynamics are also generalized from four to higher dimensions.

gr-qc↗

arXiv2023

Quantization of pseudo-hermitian systems

This work is a generalization of \cite{baldiotti2021} to Grassmann algebras of arbitrary dimensions. Here we present a covariant quantization scheme for pseudoclassical theories focused on non-hermitian quantum mechanics. The quantization maps canonically related pseudoclassical theories to equivalent quantum realizations in arbitrary dimensions. We apply the formalism to the problem of two coupled spins with Heisenberg interaction.

quant-ph↗

arXiv2023

Weyl conjecture and thermal radiation of finite systems

In this work, corrections for the Weyl law and Weyl conjecture in d dimensions are obtained and effects related to the polarization and area term are analyzed. The derived formalism is applied on the quasithermodynamics of the electromagnetic field in a finite $d$-dimensional box within a semi-classical treatment. In this context, corrections to the Stefan-Boltzmann law are obtained. Special attention is given to the two-dimensional scenario, since it can be used in the characterization of experimental setups. Another application concerns acoustic perturbations in a quasithermodynamic generalization of Debye model for a finite solid in d dimensions. Extensions and corrections for known results and usual formulas, such as the Debye frequency and Dulong-Petit law, are calculated.

quant-ph↗

arXiv2022

Repulsive Casimir force in stationary axisymmetric spacetimes

We study the influence of stationary axisymmetric spacetimes on Casimir energy. We consider a massive scalar field and analyze its dependence on the apparatus orientation with respect to the dragging direction associated with such spaces. We show that, for an apparatus orientation not considered before in the literature, the Casimir energy can change its sign, producing a repulsive force. As applications, we analyze two specific metrics: one associated with a linear motion of a cylinder and a circular equatorial motion around a gravitational source described by Kerr geometry.

quant-ph↗

arXiv2021

Classical-quantum correspondence for two-level pseudo-Hermitian systems

In this work, a classical-quantum correspondence for two-level pseudo-Hermitian systems is proposed and analyzed. We show that the presence of a complex external field can be described by a pseudo-Hermitian Hamiltonian if there is a suitable canonical transformation that links it to a real field. We construct a covariant quantization scheme which maps canonically related pseudoclassical theories to unitarily equivalent quantum realizations, such that there is a unique metric-inducing isometry between the distinct Hilbert spaces. In this setting, the pseudo-Hermiticity condition for the operators induces an involution which guarantees the reality of the corresponding symbols, even for the complex field case. We assign a physical meaning for the dynamics in the presence of a complex field by constructing a classical correspondence. As an application of our theoretical framework, we propose a damped version of the Rabi problem and determine the configuration of the parameters of the setup for which damping is completely suppressed. The experimental viability of the proposal is studied within a specific context. We suggest that the main theoretical results developed in the present work could be experimentally verified.

quant-ph↗

arXiv2019

Extended quasilocal Thermodynamics of Schwarzchild-anti de Sitter black holes

In this work we study a homogeneous and quasilocal Thermodynamics associated to the Schwarzschild-anti de Sitter black hole. The usual thermodynamic description is extended within a Hamiltonian approach with the introduction of the cosmological constant in the thermodynamic phase space. The treatment presented is consistent in as much as it respects the laws of black hole Thermodynamics and accepts the introduction of any thermodynamic potential. We are able to construct new equations of state that characterize the Thermodynamics. Novel phenomena can be expected from the proposed setup.

hep-th↗

arXiv2019

Thermodynamics of bosonic systems in adS spacetime

We analyze the thermodynamics of massless bosonic systems in D-dimensional anti-de Sitter spacetime, considering scalar, electromagnetic, and gravitational fields. Their dynamics are described by Poschl-Teller effective potentials and quantized in a unified framework, with the determination of the associated energy spectra. From the microscopic description developed, a macroscopic thermodynamic treatment is proposed, where an effective volume in anti-de Sitter geometry is defined and a suitable thermodynamic limit is considered. Partition functions are constructed for the bosonic gases, allowing the determination of several thermodynamic quantities of interest. With the obtained results, general aspects of the thermodynamics are explored.

hep-th↗

arXiv2017

A second quantized approach to the Rabi problem

In the present work the Rabi Problem, involving the response of a spin 1/2 particle subjected to a magnetic field, is considered in a second quantized approach. In this concrete physical scenario, we show that the second quantization procedure can be applied directly in a non-covariant theory. The proposed development explicits not only the relation between the full quantum treatment of the problem and the semiclassical Rabi model, but also the connection of these approaches with the Jaynes-Cummings model. The consistency of the method is checked in the semiclassical limit. The treatment is then extended to the matter component of the Rabi problem so that the Schrödinger equation is directly quantized. Considering the spinorial field, the appearance of a negative energy sector implies a specific identification between Schrödinger's and Maxwell's theories. The generalized theory is consistent, strictly quantum and non-relativistic.

quant-ph↗

arXiv2017

A Hamiltonian approach for the Thermodynamics of AdS black holes

In this work we study the Thermodynamics of D-dimensional Schwarzschild-anti de Sitter (SAdS) black holes. The minimal Thermodynamics of the SAdS spacetime is briefly discussed, highlighting some of its strong points and shortcomings. The minimal SAdS Thermodynamics is extended within a Hamiltonian approach, by means of the introduction of an additional degree of freedom. We demonstrate that the cosmological constant can be introduced in the thermodynamic description of the SAdS black hole with a canonical transformation of the Schwarzschild problem, closely related to the introduction of an anti-de Sitter thermodynamic volume. The treatment presented is consistent, in the sense that it is compatible with the introduction of new thermodynamic potentials, and respects the laws of black hole Thermodynamics. By demanding homogeneity of the thermodynamic variables, we are able to construct a new equation of state that completely characterizes the Thermodynamics of SAdS black holes. The treatment naturally generates phenomenological constants that can be associated with different boundary conditions in underlying microscopic theories. A whole new set of phenomena can be expected from the proposed generalization of SAdS Thermodynamics.

hep-th↗

arXiv2016

A Hamiltonian approach to Thermodynamics

In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac's theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases.

hep-th↗

arXiv2014

Thermodynamics of quantum photon spheres

Photon spheres, surfaces where massless particles are confined in closed orbits, are expected to be common astrophysical structures surrounding ultracompact objects. In this paper a semiclassical treatment of a photon sphere is proposed. We consider the quantum Maxwell field and derive its energy spectra. A thermodynamic approach for the quantum photon sphere is developed and explored. Within this treatment, an expression for the spectral energy density of the emitted radiation is presented. Our results suggest that photon spheres, when thermalized with their environment, have nonusual thermodynamic properties, which could lead to distinct observational signatures.

gr-qc↗

arXiv2014

Maxwell field with Torsion

We propose a generalizing gauge-invariant model of propagating torsion which couples to the Maxwell field and to charged particles. As a result we have an Abelian gauge invariant action which leads to a theory with nonzero torsion and which is consistent with available experimental data.

gr-qc↗

arXiv2010

Two and four-level systems in magnetic fields restricted in time

We describe some new exact solutions for two- and four-level systems. In all the cases, external fields have a restricted behavior in time. First, we consider two types of new solutions for one-spin equation, one of them is in a external magnetic field that acts during a finite time interval. A new solution for two interacting spins is found in the case when the field difference between the external fields in each spin vary adiabatically, vanishing on the time infinity. The latter system can be identified with a quantum gate realized by two coupled quantum dots. The probability of the Swap operation for such a gate can be explicitly expressed in terms of special functions. Using the obtained expressions, we construct plots for the Swap operation for some parameters of the external magnetic field and interaction function.

quant-ph↗

arXiv2010

Self-adjoint extensions and spectral analysis in the generalized Kratzer problem

We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional nonrelativistic motion of a particle in the potential field $V(x)=g_{1}x^{-1}+g_{2}x^{-2}$. For $g_{2}>0$ and $g_{1}<0$, the potential is known as the Kratzer potential and is usually used to describe molecular energy and structure, interactions between different molecules, and interactions between non-bonded atoms. We construct all self-adjoint Schrodinger operators with the potential $V(x)$ and represent rigorous solutions of the corresponding spectral problems. Solving the first part of the problem, we use a method of specifying s.a. extensions by (asymptotic) s.a. boundary conditions. Solving spectral problems, we follow the Krein's method of guiding functionals. This work is a continuation of our previous works devoted to Coulomb, Calogero, and Aharonov-Bohm potentials.

math-ph↗

arXiv2010

Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space

We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a $θ$-modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the $θ$-modified Dirac equation. To complete the consideration, we present a pseudoclassical model (à la Berezin-Marinov) for the corresponding nonrelativistic particle in the noncommutative space. To justify the latter model, we demonstrate that its quantization leads to the $θ$-modified Pauli equation. Then, we extract $θ$-modified interaction between a nonrelativistic spin and a magnetic field from the $θ$-modified Pauli equation and construct a $θ$-modification of the Heisenberg model for two coupled spins placed in an external magnetic field. In the framework of such a model, we calculate the probability transition between two orthogonal EPR (Einstein-Podolsky-Rosen) states for a pair of spins in an oscillatory magnetic field and show that some of such transitions, which are forbidden in the commutative space, are possible due to the space noncommutativity.

hep-th↗