arXiv subjects

E. Sadurní

Publications and source records attributed to E. Sadurní.

27 records · Page 2Linked to original sources

arXiv2016

Fundamental constraints on two-time physics

We show that generalizations of classical and quantum dynamics with two times lead to fundamentally constrained evolution. At the level of classical physics, Newton's second law is extended and exactly integrated in $1+2$ dimensional space, leading to effective single-time evolution for any initial condition. In the domain of quantum mechanics, we follow strictly the hypothesis of probability conservation by extending the Heisenberg picture to unitary evolution with two times. As a result, the observability of two temporal axes is constrained by a generalized uncertainty relation involving level spacings, total duration of the effect and Planck's constant.

quant-ph↗

arXiv2016

Stern-Gerlach splitters for lattice quasispin

We design a Stern-Gerlach apparatus that separates quasispin components on the lattice, without the use of external fields. The effect is engineered using intrinsic parameters, such as hopping amplitudes and on-site potentials. A theoretical description of the apparatus relying on a generalized Foldy-Wouthuysen transformation beyond Dirac points is given. Our results are verified numerically by means of wavepacket evolution, including an analysis of Zitterbewegung on the lattice. The necessary tools for microwave realizations, such as complex hopping amplitudes and chiral effects, are simulated.

quant-ph↗

arXiv2016

Inverse lattice design and its application to bent waveguides

This paper is divided in two parts. In the first part, the inverse spectral problem for tight-binding hamiltonians is studied. This problem is shown to have an infinite number of solutions for properly chosen energies. The space of such solutions is characterized by a hypersurface in the space of hopping amplitudes (i.e. couplings), whose dimension is half the number of sites in the array. Low dimensional examples for short chains are carefully studied and a table of exactly solvable inverse problems is provided in terms of Lie algebraic structures. With the aim of providing a method to generate lattice configurations, a set of equations for coupling constants in terms of energies is obtained; this is done by means of a new formula for the calculation of characteristic polynomials. Two examples with randomly generated spectra are studied numerically, leading to peaked distributions of couplings. In the second part of the paper, our results are applied to the design of bent waveguides, reproducing specific spectra below propagation threshold. As a demonstration, the Dirac and the finite oscillator are realized in this way. A few partially isospectral configurations are also presented.

quant-ph↗

arXiv2015

Fractal position spectrum for a class of oscillators

We show that the position operator for a class of $f$-deformed oscillators has a fractal spectrum, homeomorphic to the Cantor set, via a unitary transformation to Harper's model. The class corresponds to a choice of ergodic operators for the deformation function. Hofstadter's butterfly is plotted by direct diagonalization of a position operator with an originally vanishing diagonal. This is equivalent to a one-dimensional hamiltonian without potential.

quant-ph↗

arXiv2014

Spontaneous focusing as an emergent phenomenon

We analyze the emergence of diffractive focusing in the transition from discrete to continuous space-time variables. Three types of dynamical equations are studied in a top-to-bottom approach, starting with the most general system. First we solve a linear cellular automaton of two species, then a nearest neighbour tight-binding array and finally the time-dependent Schrödinger equation. All models are shown to produce diffractive solutions for square packet distributions. The main result of this paper is that in discrete variables, the nature of the solutions depends strongly on the size of wavepackets, whereas in continuous variables, diffraction due to discontinuities exists at every scale. A transition in the number of participants or cells is identified by means of a measure and the corresponding phenomenon is further analyzed by a generalization of Wigner functions to discrete variables and crystals.

quant-ph↗

arXiv2014

Transparent lattices and their solitary waves

We provide a familiy of transparent tight-binding models with non-trivial potentials and site-dependent hopping parameters. Their feasibility is discussed in electromagnetic resonators, dielectric slabs and quantum-mechanical traps. In the second part of the paper, the arrays are obtained through a generalization of supersymmetric quantum mechanics in discrete variables. The formalism includes a finite-difference Darboux transformation applied to the scattering matrix of a periodic array. A procedure for constructing a hierarchy of discrete hamiltonians is indicated and a particular biparametric family is given. The corresponding potentials and hopping functions are identified as solitary waves, pointing to a discrete spinorial generalization of the Korteweg-deVries family.

quant-ph↗

arXiv2013

Schematic baryon models, their tight binding description and their microwave realization

A schematic model for baryon excitations is presented in terms of a symmetric Dirac gyroscope, a relativistic model solvable in closed form, that reduces to a rotor in the non-relativistic limit. The model is then mapped on a nearest neighbour tight binding model. In its simplest one-dimensional form this model yields a finite equidistant spectrum. This is experimentally implemented as a chain of dielectric resonators under conditions where their coupling is evanescent and good agreement with the prediction is achieved.

nucl-th↗

arXiv2013

First experimental realization of the Dirac oscillator

We present the first experimental microwave realization of the one-dimensional Dirac oscillator, a paradigm in exactly solvable relativistic systems. The experiment relies on a relation of the Dirac oscillator to a corresponding tight-binding system. This tight-binding system is implemented as a microwave system by a chain of coupled dielectric disks, where the coupling is evanescent and can be adjusted appropriately. The resonances of the finite microwave system yields the spectrum of the one-dimensional Dirac oscillator with and without mass term. The flexibility of the experimental set-up allows the implementation of other one-dimensional Dirac type equations.

cond-mat.mes-hall↗

arXiv2010

Two interacting atoms in a cavity: exact solutions, entanglement and decoherence

We address the problem of two interacting atoms of different species inside a cavity and find the explicit solutions of the corresponding eigenvalues and eigenfunctions using a new invariant. This model encompasses various commonly used models. By way of example we obtain closed expressions for concurrence and purity as a function of time for the case where the cavity is prepared in a number state. We discuss the behaviour of these quantities and and their relative behaviour in the concurrence-purity plane.

quant-ph↗