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Gastón García-Calderón

Publications and source records attributed to Gastón García-Calderón.

14 recordsLinked to original sources
arXiv2026

Transient concurrence for copropagating entangled bosons and fermions

The transient dynamics of copropagating entangled bosons and fermions remain an unexplored aspect of quantum mechanics. We investigate how entanglement manifests itself in the spatiotemporal evolution of the particles using a modified version of the quantum shutter model. We derive a transient concurrence as a dynamical indicator of entanglement and demonstrate that it modulates the interference structure of the joint probability density, thereby revealing the spatial and temporal regions where probabilistic bunching and antibunching phenomena emerge. Furthermore, we derive analytical expressions revealing a structural connection between concurrence and the cosine modulation characteristic of Hanbury-Brown and Twiss (HBT) interference patterns. In the stationary limit, the Wootters concurrence is shown to coincide with the interferometric visibility of the resulting pattern. This work establishes a structural bridge between entanglement signatures and interference phenomena in transient copropagating systems, providing a theoretical framework for exploring their dynamical interplay.

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arXiv2019

Effect of the resonance spectra in the propagation of two decaying entangled particles

An exact analytical solution of the decaying wave function of two identical noninteracting particles, which are entangled by spatial symmetry, is used to analyze the effect of the resonance spectra in the propagation of the decaying probability density outside the interaction potential region. We find, using exactly solvable problems, that a usual approximation that considers the two resonance levels associated with the initial states, is affected substantially in the case of sharp high energy resonances by disrupting the pure exponential decaying regime exhibited by the two resonance level approximation, whereas for broad high energy resonances, we find that the probability density profile is well described by the two resonance approximation.

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arXiv2019

The exponential-nonexponential transition in quantum decay as a phenomenon of interference in time domain of the decaying particle with itself

By using an exact analytical non-Hermitian approach in terms of resonance (quasinormal) states we express the decaying wave function as the sum of exponential and nonexponential decaying solutions to the time-dependent Schrödinger equation. We show that the exponential-nonexponential transition of decay at long times represents physically a process of interference in time domain of the decaying particle with itself.

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arXiv2019

Heisenberg uncertainty relations for the non-Hermitian resonance state solutions to the Schrödinger equation

Resonance (quasinormal) states correspond to non-Hermitian solutions to the Schrödinger equation obeying outgoing boundary conditions which lead to complex energy eigenvalues and momenta. Following the normalization rule for resonance states obtained from the residue at a complex pole of the outgoing Green's function to the problem, we propose a definition of expectation value for these states and use it to investigate the extent of validity of the Heisenberg uncertainty relations for potentials that vanish after a distance. We derive analytical expressions for the expectation values involving the momentum and the position for a given resonance state and find in model calculations that the Heisenberg uncertainty relations are satisfied for a broad range of potential parameters. A comparison of our approach with that based on the regularization method by Zel'dovich yields very similar results except for resonance energies very close to the energy threshold. Our work shows that the validity of the Heisenberg uncertainty relations may be extended to the non-Hermitian resonance state solutions to the Schrödinger equation.

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arXiv2017

Exact analytical non-Hermitian formulation of the time evolution of decay of one and two identical quantum particles

An analytical solution to the time evolution of decay of one and two identical noninteracting particles is presented using the formalism of resonant states. It is shown that the time-dependent wave function and hence the survival and nonescape probabilities for the initial state of a single particle and entangled symmetric and antisymmetric initial states of two identical particles evolve in a distinctive form along the exponential and long-time nonexponential decaying regimes. In particular, for the last regime, they exhibit different inverse power of time behaviors.

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arXiv2017

Underlying non-Hermitian character of the Born rule in open quantum systems

The absolute value squared of the probability amplitude corresponding to the overlap of an initial state with a continuum wave solution to the Schrödinger equation of the problem, has the physical interpretation provided by the Born rule. Here, it is shown that for an open quantum system, the above probability may be written in an exact analytical fashion as an expansion in terms of the non-Hermitian resonance (quasinormal) states and complex poles to the problem which provides an underlying non-Hermitian character of the Born rule.

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arXiv2017

Nonexponential tunneling decay of a single ultracold atom

By using an exact analytical approach to the time evolution of decay we investigate the tunneling decay of ultracold single atoms, to discuss the conditions for deviations of the exponential decay law. We find that $R$, given by the ratio of the energy of the decaying fragment $\mathcal{E}_r$ to its corresponding width $Γ_r$, is the relevant quantity in this study. When $R$ is less than $0.3$ the decay of the atom goes to a good approximation for the first few lifetimes as $\exp(-Γ_rt/2\hbar)t^{-3/2}$. We also find that for values of $R \sim 1$, the nonexponential behavior occurs in a post-exponential regime that goes as $t^{-3}$ after around a dozen of lifetimes. The above conditions depend on suitable designed potential parameters and suggest that for values $R \lesssim 1$, the experimental verification of nonexponential decay might be possible.

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arXiv2016

Time evolution of decay for purely absorptive potentials: The effect of spectral singularities

We consider an analytical approach that involves the complex poles of the propagator to investigate the effect due to the lack of time reversal invariance on the time evolution of decay for purely absorptive potentials. We find that the choice of the initial state may change the exponential decaying regime into a nonexponential oscillatory behavior at time scales of the order of a lifetime of the system. We illustrate this effect for a spectral singularity corresponding to a purely imaginary delta-shell potential.

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arXiv2013

Analytical study of quadratic and non-quadratic short-time behavior of quantum decay

The short-time behavior of quantum decay of an unstable state initially located within an interaction region of finite range is investigated using a resonant expansion of the survival amplitude. It is shown that in general the short-time behavior of the survival probability $S(t)$ has a dependence on the initial state and may behave either as $S(t)=1-\mathcal{O}(t^{3/2})$ or as $S(t)=1-\mathcal{O}(t^{2})$. The above cases are illustrated by solvable models. The experiment reported in Ref. [1] does not distinguish between the above short-time behaviors.

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arXiv2012

Hermitian and non-Hermitian formulations of the time evolution of quantum decay

This work discusses Hermitian and non-Hermitian formulations for the time evolution of quantum decay, that involve respectively, continuum wave functions and resonant states, to show that they lead to an identical description for a large class of well behaved potentials. Our approach is based on the analytical properties of the outgoing Green's function to the problem in the complex wave number plane.

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arXiv2011

Time evolution of decay of two identical quantum particles

An analytical solution for the time evolution of decay of two identical non interacting quantum particles seated initially within a potential of finite range is derived using the formalism of resonant states. It is shown that the wave function, and hence also the survival and nonescape probabilities, for factorized symmetric and entangled symmetric/antisymmetric initial states evolve in a distinctive form along the exponentially decaying and nonexponential regimes. Our findings show the influence of the Pauli exclusion principle on decay. We exemplify our results by solving exactly the s-wave delta shell potential model.

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arXiv2005

Quantum shutter approach to tunneling time scales with wave packets

The quantum shutter approach to tunneling time scales (G. Garc\'{ı}a-Calderón and A. Rubio, Phys. Rev. A \textbf{55}, 3361 (1997)), which uses a cutoff plane wave as the initial condition, is extended in such a way that a certain type of wave packet can be used as the initial condition. An analytical expression for the time evolved wave function is derived. The time-domain resonance, the peaked structure of the probability density (as the function of time) at the exit of the barrier, originally found with the cutoff plane wave initial condition, is studied with the wave packet initial conditions. It is found that the time-domain resonance is not very sensitive to the width of the packet when the transmission process is in the tunneling regime.

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arXiv2003

Transient time-domain resonances and the time scale for tunneling

Transient {\it time-domain resonances} found recently in time-dependent solutions to Schrödinger's equation are used to investigate the issue of the tunneling time in rectangular potential barriers. In general, a time frequency analysis shows that these transients have frequencies above the cutoff frequency associated with the barrier height, and hence correspond to non-tunneling processes. We find, however, a regime characterized by the barrier opacity, where the peak maximum $t_{max}$ of the {\it time-domain resonance} corresponds to under-the-barrier tunneling. We argue that $t_{max}$ represents the relevant tunneling time scale through the classically forbidden region.

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