arXiv subjects

Naivo Rabesiranana

Publications and source records attributed to Naivo Rabesiranana.

5 recordsLinked to original sources

arXiv2026

Geometry-Driven Thermodynamics: Shape Effects and Anisotropy in Quantum-Confined Ideal Fermi and Bose Gases

This study presents a unified description of the thermodynamics of ideal quantum gases under nanoscale confinement using a Quantum Phase Space (QPS) formalism. We show that the statistical momentum variances B_ll capture quantum degeneracy: for fermions, they incorporate the Fermi energy, and for bosons, the condensate energy scale. This bridges our formalism with established results and allows both Fermi-Dirac and Bose-Einstein statistics to be treated within a single framework. From this, we derive exact analytical expressions for key properties - internal energy, anisotropic pressure tensor, and heat capacity - seamlessly describing the transition from classical to quantum regimes. Our results reveal that nanoscale thermodynamics is intrinsically anisotropic: pressure becomes direction-dependent, with fractional anisotropy reaching unity under extreme confinement. Notably, pure shape effects, controlled via geometric parameters in B_ll, enable manipulation of phase transitions without altering system size, temperature, or density. Numerical simulations for confined electron and helium-4 gases show significant quantum effects at accessible temperatures (mK to K) for confinement scales of 5-50 nm. This work provides a theoretical toolkit for nanosystems, with direct implications for nanofluidic devices and quantum sensors.

cond-mat.quant-gas↗

arXiv2025

Joint momenta-coordinates states as pointer states in quantum decoherence

Quantum decoherence provides a framework to study the emergence of classicality from quantum systems by showing how interactions with the environment suppress interferences and select robust states known as pointer states. Earlier studies have linked Gaussian coherent states to pointer states. More recently, it was conjectured that more general quantum states called joint momenta-coordinates states may serve as more suitable candidates to be pointer states. These states are associated to the concept of quantum phase space and saturate, by definition, generalized uncertainty relations. In this work, we rigorously prove this conjecture. Building on the Lindblad framework for the damped harmonic oscillator, and applying Zurek's predictability-sieve criterion, we analyze both underdamped and overdamped regimes. We show that only in the underdamped case do joint momenta-coordinates states remain pure and robust for all times, establishing them as the true pointer states. This extends Isar's earlier underdamped treatment, generalizes the concept beyond Gaussian approximations, and embeds classical robustness in the quantum phase space formalism, with potential applications in error-resistant quantum information.

quant-ph↗

arXiv2025

Quantum Phase Space Approach to the Ideal Fermi and Bose Gases

In this work, improvements are introduced to the current models of the ideal Fermi gas and the ideal Bose gas by incorporating the quantum nature of phase space, which is directly linked to the uncertainty principle. These improved models build upon the recently developed concepts of quantum phase space (QPS) and the QPS representation of quantum mechanics. The Hamiltonian operator for a gas particle and its eigenstates are first determined, and quantum statistical mechanics is used to derive the thermodynamic properties of the ideal gas. Analytic expressions for thermodynamic quantities&#8212including the grand canonical potential, particle number, internal energy, von Neumann entropy, and pressure&#8212are derived, along with the corresponding thermodynamic equations of state for both bosons and fermions. These corrections are particularly significant at low temperatures and in confined volumes, where quantum effects related to system geometry, such as shape and size, become significant. The results also establish a direct link between thermodynamic functions and the quantum statistical variances of momentum. Importantly, the improved models recover well-known classical relations of the ideal gas in the high-temperature and large-volume limits, ensuring consistency with classical physics. By addressing quantum corrections and their thermodynamic implications, this work provides a foundation for further applications in nanoscale systems, quantum gases, low-temperature physics, ultracold physics, and astrophysics.

cond-mat.quant-gas↗

arXiv2023

Highlighting relations between Wave-particle duality, Uncertainty principle, Phase space and Microstates

Wave-particle duality is often considered as the modern answer to the problem of the nature of light after more than 2000 years of questioning. It is also the answer given by quantum physics concerning the nature of matter particles and any other radiations. The main objective of this work is to analyze the relations that are existing between this concept of wave-particle duality, the uncertainty principle and the concepts of phase space and microstates considered in statistical mechanics. It is mainly highlighted that while the concepts of phase space and microstates were already introduced in classical physics before the discovery of the wave-particle duality, a correct understanding of them cannot be achieved without the use of the concept of quantum phase space and phase space representation of quantum mechanics which are directly related to the uncertainty principle. The possibility of using these concepts of quantum phase space and phase space representations of quantum mechanics to help in a deeper description of the wave-particle duality and in the study of some current issues related to foundational problems of quantum mechanics like quantum decoherence and the measurement problem is also discussed.

quant-ph↗

arXiv2023

Quantum and Relativistic corrections to Maxwell-Boltzmann ideal gas model from a Quantum Phase Space approach

The quantum corrections related to the ideal gas model that are often considered are those which are related to the particles nature: bosons or fermions. These corrections lead respectively to the Bose-Einstein and Fermi-Dirac statistics. However, in this work, other kinds of corrections which are related to the quantum nature of phase space are considered. These corrections are introduced as improvement in the expression of the partition function of an ideal gas. Then corrected thermodynamics properties of the gas are deduced. Both the non-relativistic quantum and relativistic quantum cases are considered. It is shown that the corrections in the non-relativistic quantum case may be particularly useful to describe the deviation from classical behavior of a Maxwell-Boltzmann gas at low temperature and in confined space. These corrections can be considered as including the description of quantum size and shape effects. For the relativistic quantum case, the corrections could be relevant for confined space and when the thermal energy of each particle is comparable to their rest energy. The corrections appear mainly as modifications in the thermodynamic equation of state and in the expressions of the partition function and thermodynamic functions like entropy, internal energy, and free energy. Classical expressions are obtained as asymptotic limits.

cond-mat.stat-mech↗