arXiv subjects

Alberto G. Rojo

Publications and source records attributed to Alberto G. Rojo.

13 recordsLinked to original sources

arXiv2026

Nonholonomic constraints at finite temperature

We investigate the behavior of dynamical systems with nonholonomic constraints when coupled to a thermal bath, focusing on the paradigmatic case of the Chaplygin sleigh. A straightforward Langevin-type approach obtained by naively adding stochastic and dissipative terms to the equations of motion predicts a regime in which useful work can be extracted, violating the second law of thermodynamics. To resolve this paradox, we resort to a physically motivated implementation of the nonholonomic constraint as the limiting case of a viscous interaction. However, at finite temperature, fluctuation-dissipation relations imply that the viscous force has to be complemented with stochastic forces acting at the contact. We show that their incorporation restores compliance with the second law. Therefore, our results place fundamental limits on the physical realizability of idealized nonholonomic constraints.

cond-mat.stat-mech↗

arXiv2026

Self-Force of a Dirac String: An Explicit Calculation

A Dirac string can be modeled as a semi-infinite solenoid carrying a fixed magnetic flux. Dirac pointed out that such a string should experience a nonvanishing and divergent self-force, but explicit calculations are rarely shown. Motivated by a recent comment by McDonald, we present a direct and elementary derivation of this self-force. Treating the string as a stack of current loops, we compute the axial force produced by the radial magnetic field generated by the rest of the solenoid. The resulting force, $F=Φ^2/(2πμ_0 a^2)$, diverges as the solenoid radius $a\to0$ with flux $Φ$ fixed, making explicit the singular nature of the Dirac string.

physics.class-ph↗

arXiv2025

Coulomb force between two Dirac monopoles

The model of magnetic monopoles that was proposed by Paul Dirac in 1931 has long been a subject of theoretical interest in physics because of its potential to explain the quantization of electric charge. While much attention has been given to non-Dirac monopoles, Dirac's model, which involves an infinitely thin solenoid known as a Dirac string, presents subtleties in the interaction between monopoles. In this paper, we show that the force between two Dirac monopoles obeys a Coulomb-like interaction law. This derivation offers an instructive exercise in fundamental electromagnetism concepts and is appropriate for undergraduate and early graduate-level students.

physics.class-ph↗

arXiv2025

What is the maximum radius of cold planets?

Planets have maximum radii close to that of Jupiter. Qualitatively, the reason for this maximum size is that, as one adds mass, the force of gravity becomes sufficiently strong to cause the radius to decrease. We show that this effect can be understood quantitatively using a simple variational principle very similar to that used to compute the size of the hydrogen atom.

astro-ph.IM↗

arXiv2025

Common principles behind rainbows and boat wakes

Rainbows and boat wakes may seem unrelated, but they share deep mathematical connections through ray folding, caustics, and Airy interference. This paper explores these principles, which are also relevant for explaining phenomena such as shimmering effects on the bottom of pools and twinkling stars. By revisiting Airy's theories on wavefronts and caustics, we demonstrate their applications not only in optics and for water waves but also in quantum wave packets. Using concepts from undergraduate physics, we highlight the universal patterns that unify these diverse phenomena.

physics.pop-ph↗

arXiv2023

The chiral knife edge: a simplified rattleback to illustrate spin inversion

We present the chiral knife edge rattleback, an alternative version of previously presented systems that exhibit spin inversion. We offer a full treatment of the model using qualitative arguments, analytical solutions as well as numerical results. We treat a reduced, one--mode problem which not only contains the essence of the physics of spin inversion, but that also exhibits an unexpected connection to the Chaplygin sleigh, providing new insight into the non-holonomic structure of the problem. We also present exact results for the full problem together with estimates of the time between inversions that agree with previous results in the literature.

physics.pop-ph↗

arXiv2010

Matrix exponential solution of the Landau-Zener problem

We present a derivation of the Landau-Zener solution through the explicit evaluation of the time ordered propagator. The result is exact and does not involve the solution of the differential equation for the spin amplitudes.

quant-ph↗

arXiv2009

The rolling sphere and the quantum spin

We consider the problem of a sphere rolling of a curved surface and solve it by mapping it to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. The mapping can be of pedagogical use in discussing both rolling and spin precession, and in particular in understanding the emergence of geometrical phases in classical problems.

physics.class-ph↗

arXiv2009

The Parallelometer: a mechanical device to study curvature

A simple mechanical device is introduced, the parallelometer, that can be used to measure curvatures of surfaces. The device can be used as a practical illustration of parallel transport of a vector and to study Berry phase shift when it is carried along a loop on the surface. Its connection to the Foucault pendulum is discussed. The experimental results can be successfully compared with the theoretical expectations. The experiment is inexpensive and conceptually easy to perform and understand for a beginner.

gr-qc↗

arXiv2006

A Cold Atomic Fermi Gas with a Spatially Modulated Interaction

We study an ultra-cold atomic Fermi Gas with the atom-atom interaction modulated periodically in space. A novel ground state with cooper pairs occupying non-zero center of mass momenta is found. Such a state is closely related to the state proposed by Fulde, Ferrell, Larkin, and Ovchinnikov(FFLO). The resultant single particle excitations with momenta along the direction of the modulation shows multiple-gap structures. Such a system can be realized in experiment with a spatially modulated Feshbach resonance. Experimental signatures of such a state are discussed.

cond-mat.supr-con↗

arXiv2005

Hamilton's principle: why is the integrated difference of kinetic and potential energy minimized?

I present an intuitive answer to an often asked question: why is the integrated difference K-U between the kinetic and potential energy the quantity to be minimized in Hamilton's principle? Using elementary arguments, I map the problem of finding the path of a moving particle connecting two points to that of finding the minimum potential energy of a static string. The mapping implies that the configuration of a non--stretchable string of variable tension corresponds to the spatial path dictated by the Principle of Least Action; that of a stretchable string in space-time is the one dictated by Hamilton's principle. This correspondence provides the answer to the question above: while a downward force curves the trajectory of a particle in the (x,t) plane downward, an upward force of the same magnitude stretches the string to the same configuration x(t).

physics.ed-ph↗

arXiv2001

Gyroscopic Classical and Quantum Oscillators interacting with Heat Baths

We analyze the stability of a gyroscopic oscillator interacting with a finite- and infinite-dimensional heat bath in both the classical and quantum cases. We consider a finite gyroscopic oscillator model of a particle in a magnetic field and examine the stability before and after coupling to a heat bath. It is shown that if the oscillator is gyroscopically stable, coupling to a sufficiently massive heat bath induces instability. The meaning of these ideas in the quantum context is discussed. The model extends the exact diagonalization analysis of an oscillator and field of Ford, Lewis, and O'Connell to the gyroscopic setting.

cond-mat.stat-mech↗

arXiv2000

Control of Squeezed States

In this paper we consider the classical and quantum control of squeezed states of harmonic oscillators. This provides a method for reducing noise below the quantum limit and provides an example of the control of under-actuated systems in the stochastic and quantum context. We consider also the interaction of a squeezed quantum oscillator with an external heat bath.

cond-mat.stat-mech↗