arXiv subjects

Enric Pérez

Publications and source records attributed to Enric Pérez.

6 recordsLinked to original sources

arXiv2026

Between equilibrium and fluctuation: Einstein's heuristic argument and Boltzmann's principle

We critically revisit Einstein's 1905 heuristic argument for lightquanta, considering its internal coherence and the scope of its applicability. We argue that Einstein's reasoning, often celebrated for its originality, is ambiguous because it can be understood as a fluctuation or as a comparison between equilibrium states. A historical and conceptual analysis of Einstein's use of Boltzmann's principle in those years reveals his evolving stance on its meaning and the role of probability, as well as his persistent doubts about the nature of radiation. We use our analysis to examine the limitations of extending the notion of Einstein's lightquanta across the electromagnetic spectrum: the relevant parameter is not the frequency, but the occupancy number.

physics.hist-ph↗

arXiv2025

Blurred orbits and blurred particles: Heisenberg's 1926 helium atom

This work analyses the extent to which the "blurred orbits" of the current model for the atom, drafted by Heisenberg in 1926, fits the image of a bunch of wandering electrons around a nucleus. We will deal with early appearances of the concept of indistinguishable particles within the frame of quantum mechanics. There are few studies on the use of this concept in Heisenberg's 1926 papers on helium, in contrast with the large number of them on its use in Bose--Einstein's 1924 papers. We will discuss to what extent Heisenberg's approach leads to a purely statistical interpretation of this concept. We will also study the viewpoint of Dirac, who dealt with the same topic few months later. Although the indistinguishability of the electrons and indeterminacy are common explanations for the blurring of electron orbits, we argue that such an image is an oversimplification which masks interesting aspects of: a) the dynamics of bound electrons and b) the deeper implications of indistinguishability in quantum mechanics.

physics.hist-ph↗

arXiv2015

Ehrenfest's adiabatic hypothesis in Bohr's quantum theory

It is widely known that Paul Ehrenfest formulated and applied his adiabatic hypothesis in the early 1910s. Niels Bohr, in his first attempt to construct a quantum theory in 1916, used it for fundamental purposes in a paper which eventually did not reach the press. He decided not to publish it after having received the new results by Sommerfeld in Munich. Two years later, Bohr published "On the quantum theory of line-spectra." There, the adiabatic hypothesis played an important role, although it appeared with another name: the principle of mechanical transformability. In the subsequent variations of his theory, Bohr never suppressed this principle completely. We discuss the role of Ehrenfest's principle in the works of Bohr, paying special attention to its relation to the correspondence principle. We will also consider how Ehrenfest faced Bohr's uses of his more celebrated contribution to quantum theory, as well as his own participation in the spreading of Bohr's ideas.

physics.hist-ph↗

arXiv2014

A Grasp of Identity

We revisit the treatment of identical particles in quantum mechanics. Two kinds of solutions of Schrödinger equation are found and analyzed. First, the known symmetrized and antisymmetrized eigenfunctions. We examine how the very concept of particle is blurred whithin this approach. Second, we propose another kind of solution with no symmetries that we identify with Maxwell-Boltzmann statistics. In it, particles do preserve their individuality, as they are provided with individual energy and momenta. However, these properties cannot be univocally ascribed; moreover, particles do not possess distinctive positions. Finally, we explore how these results affect the calculation of canonical partition function, and we show that extensivity arises as a consequence of identity.

quant-ph↗

arXiv2013

Classical limit of the canonical partition function

We analyze the so-called classical limit of the quantum-mechanical canonical partition function. In order to do that, we define accurately the density matrix for symmetrized and antisymmetrized wave functions only (Bose-Einstein and Fermi-Dirac), and find an exact relation between them and the density matrix for non symmetrized functions (Maxwell-Boltzmann). Our results differ from the generally assumed in a numerical factor N!, for which we suggest a physical interpretation. We derive as well the reverse (and also exact) relation, to find the canonical partition function for non-symmetrized wave functions in terms of the corresponding function for fermions and bosons.

cond-mat.stat-mech↗

arXiv2010

Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics

In this article, we analyze the third of three papers, in which Einstein presented his quantum theory of the ideal gas of 1924-1925. Although it failed to attract the attention of Einstein's contemporaries and although also today very few commentators refer to it, we argue for its significance in the context of Einstein's quantum researches. It contains an attempt to extend and exhaust the characterization of the monatomic ideal gas without appealing to combinatorics. Its ambiguities illustrate Einstein's confusion with his initial success in extending Bose's results and in realizing the consequences of what later became to be called Bose-Einstein statistics. We discuss Einstein's motivation for writing a non-combinatorial paper, partly in response to criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments are based on Einstein's belief in the complete analogy between the thermodynamics of light quanta and of material particles and invoke considerations of adiabatic transformations as well as of dimensional analysis. These techniques were well-known to Einstein from earlier work on Wien's displacement law, Planck's radiation theory, and the specific heat of solids. We also investigate the possible role of Ehrenfest in the gestation of the theory.

physics.hist-ph↗