arXiv subjects

Wilfrid Chrysante Solofoarisina

Publications and source records attributed to Wilfrid Chrysante Solofoarisina.

6 recordsLinked to original sources

arXiv2026

Extension of the Shockley-Queisser Limit for Nanostructured Solar Cells

This article extends the Shockley-Queisser limit to nanostructured solar cells using the quantum phase space formalism. The parameter B_ll represents the momentum variance in each confinement direction and acts as a variance-covariance matrix linking the nanostructure geometry to thermodynamic properties. Electron-electron interactions are included via an exchange-correlation energy with an adjustable coefficient theta. The authors derive an analytical expression for the maximum efficiency as a function of size, shape, temperature, and doping. For the cylindrical geometry, the exact confinement energy uses the first zero of the Bessel function j_0,1. Numerical simulations are performed with Python 3.8.1, NumPy, and Matplotlib for PbS quantum dots in four geometries: cube, square parallelepiped, cylinder, and sphere. The integral is evaluated using an exact convergent series expansion. Results show that the maximum efficiency reaches 48.7 percent for a 5 nanometre cube, 49.0 percent for flattened parallelepiped and cylinder shapes, and 49.1 percent for a 3 nanometre sphere. These values greatly exceed the bulk PbS efficiency of 15.8 percent and surpass classical Shockley-Queisser limits. For constant-volume shapes, two efficiency peaks appear corresponding to different aspect ratios. The model correctly returns to classical values for large sizes. This approach provides a theoretical framework for optimising nanostructured solar cells and demonstrates that quantum confinement offers a promising route to surpass traditional photovoltaic limits.

cond-mat.mes-hall↗

arXiv2026

Geometric structure of the relativistic quantum phase space

The quest to reconcile quantum mechanics with gravitational theory motivates the exploration of frameworks that treat quantum uncertainty and spacetime geometry under a unified approach. A promising candidate that emerges from this pursuit is the relativistic quantum phase space (QPS) formalism, which extends classical phase space by incorporating both mean values and variance-covariance matrices of quantum states, providing a unified setting where the uncertainty principle and relativistic covariance coexist. For the signature $(1,4)$, we construct a scalar from the mean values and the inverse variance-covariance matrix and prove its invariance under linear canonical transformations (LCTs). Motivated by the form of the variance-covariance matrix in a particular reference frame, we identify this invariant as $Γ= L^2/\ell^2$ for states that saturate the uncertainty relations, where $L$ and $\ell$ are two fundamental length scales that can be identified with the de Sitter radius and the Planck length, respectively. From this invariant, we obtain a geometric equation that unifies mean values and quantum fluctuations. In the limit $\ell \to 0$, the equation reduces to the de Sitter spacetime equation; in the limit $L \to \infty$, it yields a curved momentum space reminiscent of Born reciprocity. In the Minkowski limit (both $\ell \to 0$ and $L \to \infty$), the familiar relativistic relations for rest mass and proper time emerge. These limiting cases show how the Planck length and the cosmological constant can be unified within a single geometric constraint, establishing the QPS geometry as a promising framework for exploring the interplay between quantum mechanics and gravity.

quant-ph↗

arXiv2026

Casimir operators for the relativistic quantum phase space symmetry group

Recent developments in the unification of quantum mechanics and relativity have emphasized the necessity of generalizing classical phase space into a relativistic quantum phase space which is a framework that inherently incorporates the uncertainty principle and relativistic covariance. In this context, the present work considers the derivation of linear and quadratic Casimir operators corresponding to representations of the Linear Canonical Transformations (LCT) group associated with a five-dimensional spacetime of signature (1,4). This LCT group, which emerges naturally as the symmetry group of the relativistic quantum phase space, is isomorphic to the symplectic group Sp(2,8). The latter notably contains the de Sitter group SO(1,4) as a subgroup. This geometric setting provides a unified framework for extending the Standard Model of particle physics while incorporating cosmological features. Previous studies have shown that the LCT group admits both fermionic-like and bosonic-like representations. Within this framework, a novel classification of quarks and leptons, including sterile neutrinos, has also been proposed. In this work, we present a systematic derivation of the linear and quadratic Casimir operators associated with these representations, motivated by their fundamental role in the characterization of symmetry groups in physics. The construction is based on the relations between the LCT group and the pseudo-unitary group U(1,4). Three linears and three quadratics Casimir operators are identified: two corresponding to the fermionic-like representation, two to the bosonic-like representation, and two hybrid operators linking the two representations. The complete eigenvalue spectra and corresponding eigenstates for each operator are subsequently computed and identified

quant-ph↗

arXiv2026

Contractions of the relativistic quantum LCT group and the emergence of spacetime symmetries

Advances in the study of relativistic quantum phase space have established the set of Linear Canonical Transformations (LCTs) as a candidate for the fundamental symmetry group associated with relativistic quantum physics. In this framework, for a spacetime of signature $(N_+,N_-)$, the symmetry of the relativistic quantum phase space is described by the LCT group, isomorphic to the symplectic Lie group $Sp(2N_+,2N_-)$, which preserves the canonical commutation relations (CCRs) and treats spacetime coordinates and momenta operators on an equal footing. In this work, we investigate the contraction structure of the Lie algebra associated with the LCT group for signature $(1,4)$, clarifying how familiar spacetime symmetry groups emerge from this more fundamental quantum phase space symmetry. Using the Inönü-Wigner group contraction formalism, we examine each limit case corresponding to the possible combinations of asymptotic values of two fundamental length scale parameters associated with the theory, namely a minimum length $\ell$ and a maximum length $L$, which may be identified respectively with the Planck length and the de Sitter radius. We explicitly analyze how contractions of the LCT Lie algebra lead to the physically relevant de Sitter algebra $\mathfrak{so}(1,4)$ and, in the flat-curvature limit, to the Poincaré algebra $\mathfrak{iso}(1,3)$ of four-dimensional spacetime. This provides an explicit mechanism through which relativistic spacetime symmetry can emerge from a deeper symplectic structure of quantum phase space.

quant-ph↗

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↗

arXiv2015

Study on linear canonical transformation in a framework of a phase space representation of quantum mechanics

We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work [1]. We begin with a brief recall about the so called phase space representation. We give the definition of linear canonical transformation with the transformation law of coordinate and momentum operators. We establish successively the transformation laws of mean values, dispersions, basis state and wave functions.Then we introduce the concept of isodispersion linear canonical transformation.

quant-ph↗