arXiv subjects

J. G. Dueñas

Publications and source records attributed to J. G. Dueñas.

6 recordsLinked to original sources

arXiv2025

$\texttt{Symdyn}$: an automated algebraic solution for high-order quantum systems

Many significant quantum physical systems are characterized by Hamiltonians expressible as a linear combination of time-independent generators of a closed Lie algebra, $\hat{H}(t)=\sum_{l=1}^{L}η_{l}(t)\hat{g}_{l}$. The Wei-Norman method provides a framework for determining the coefficients of the corresponding time evolution operator in its factorized representation, $\hat{U}(t) = \prod_{l=1}^{L} e^{ Λ_{l}(t)\hat{g}_{l}}$. This work introduces $\texttt{Symdyn}$, a Python library that automates the application of this method. The library efficiently computes similarity transformations and the nonlinear differential equations intrinsic to derive Baker-Campbell-Hausdorff-like relations and the time evolution of high-order quantum systems ($L\geq 6$). We demonstrate its robustness by deriving the time evolution operator for a system of two time-dependent coupled harmonic oscillators. Additionally, we specialize the library to the Lie group $\textit{SU}(N)$, showing its versatility with $\textit{SU}(2)$, $\textit{SU}(3)$ and $\textit{SU}(4)$ examples, relevant to quantum computing.

quant-ph↗

arXiv2016

Boundary effects on radiative processes of two entangled atoms

We analyze radiative processes of a quantum system composed by two identical two-level atoms interacting with a massless scalar field prepared in the vacuum state in the presence of perfect reflecting flat mirrors. We consider that the atoms are prepared in a stationary maximally entangled state. We investigate the spontaneous transitions rates from the entangled states to the collective ground state induced by vacuum fluctuations. In the empty-space case, the spontaneous decay rates can be enhanced or inhibited depending on the specific entangled state and changes with the distance between the atoms. Next, we consider the presence of perfect mirrors and impose Dirichlet boundary conditions on such surfaces. In the presence of a single mirror the transition rate for the symmetric state undergoes a slight reduction, whereas for the antisymmetric state our results indicate a slightly enhancement. Finally, we investigate the effect of multiple reflections by two perfect mirrors on the transition rates.

quant-ph↗

arXiv2014

Thermodynamics of the Bosonic Randomized Riemann Gas

The partition function of a bosonic Riemann gas is given by the Riemann zeta function. We assume that the hamiltonian of this gas at a given temperature $β^{-1}$ has a random variable $ω$ with a given probability distribution over an ensemble of hamiltonians. We study the average free energy density and average mean energy density of this arithmetic gas in the complex $β$-plane. Assuming that the ensemble is made by an enumerable infinite set of copies, there is a critical temperature where the average free energy density diverges due to the pole of the Riemann zeta function. Considering an ensemble of non-enumerable set of copies, the average free energy density is non-singular for all temperatures, but acquires complex values in the critical region. Next, we study the mean energy density of the system which depends strongly on the distribution of the non-trivial zeros of the Riemann zeta function. Using a regularization procedure we prove that the this quantity is continuous and bounded for finite temperatures.

math-ph↗

arXiv2014

One-loop effective action and the Riemann Zeros

We present a remarkable connection between the asymptotic behavior of the Riemann zeros and one-loop effective action in Euclidean scalar field theory. We show that in a two-dimensional space, the asymptotic behavior of the Fourier transform of two-point correlation functions fits the asymptotic distribution of the non-trivial zeros of the Riemann zeta function. We work out an explicit example, namely the non-linear sigma model in the leading order in $1/N$ expansion.

math-ph↗

arXiv2014

Casimir Energy Corrections by Light-Cone Fluctuations

We study the effects of light-cone fluctuations on the renormalized zero-point energy associated with a free massless scalar field in the presence of boundaries. In order to simulate light-cone fluctuations we introduce a space-time dependent random coefficient in the Klein-Gordon operator. We assume that the field is defined in a domain with one confined direction. For simplicity, we choose the symmetric case of two parallel plates separated by a distance $a$. The correction to the renormalized vacuum energy density between the plates goes as $1/a^{8}$ instead of the usual $1/a^{4}$ dependence for the free case. In turn we also show that light-cone fluctuations break down the vacuum pressure homogeneity between the plates.

hep-th↗

arXiv2013

Riemann zeta zeros and zero-point energy

We postulate the existence of a self-adjoint operator associated to a system with countably infinite number of degrees of freedom whose spectrum is the sequence of the nontrivial zeros of the Riemann zeta function. We assume that it describes a massive scalar field coupled to a background field in a $(d+1)$-dimensional flat space-time. The scalar field is confined to the interval $[0,a]$ in one dimension and is not restricted in the other dimensions. The renormalized zero-point energy of this system is presented using techniques of dimensional and analytic regularization. In even dimensional space-time, the series that defines the regularized vacuum energy is finite. For the odd-dimensional case, to obtain a finite vacuum energy per unit area we are forced to introduce mass counterterms. A Riemann mass appears, which is the correction to the mass of the field generated by the nontrivial zeros of the Riemann zeta function.

hep-th↗