arXiv subjects

Gonzalo Ordonez

Publications and source records attributed to Gonzalo Ordonez.

25 records · Page 2Linked to original sources

arXiv2011

Resonant Spectrum Analysis of the Conductance of Open Quantum System and Three Types of Fano Parameter

We explain the Fano peak (an asymmetric resonance peak) as an interference effect involving resonant states. We reveal that there are three types of Fano asymmetry according to their origins: the interference between a resonant state and an anti-resonant state, that between a resonant state and a bound state, and that between two resonant states. We show that the last two show the asymmetric energy dependence given by Fano, but the first one shows a slightly different form. In order to show the above, we analytically and microscopically derive a formula where we express the conductance purely in terms of the summation over all discrete eigenstates including resonant states and anti-resonant states, without any background integrals. We thereby obtain microscopic expressions of the Fano parameters that describe the three types of the Fano asymmetry. One of the expressions indicate that the corresponding Fano parameter becomes complex under an external magnetic field.

cond-mat.mes-hall↗

arXiv2010

Resonant-state expansion of the Green's function of open quantum systems

Our series of recent work on the transmission coefficient of open quantum systems in one dimension will be reviewed. The transmission coefficient is equivalent to the conductance of a quantum dot connected to leads of quantum wires. We will show that the transmission coefficient is given by a sum over all discrete eigenstates without a background integral. An apparent "background" is in fact not a background but generated by tails of various resonance peaks. By using the expression, we will show that the Fano asymmetry of a resonance peak is caused by the interference between various discrete eigenstates. In particular, an unstable resonance can strongly skew the peak of a nearby resonance.

cond-mat.mes-hall↗

arXiv2009

Existence and nonexistence of an intrinsic tunneling time

Using a time operator, we define a tunneling time for a particle going through a barrier. This tunneling time is the average of the phase time introduced by other authors. In addition to the delay time caused by the resonances over the barrier, the present tunneling time is also affected by the branch point at the edge of the energy continuum. We find that when the particle energy is near the branch point, the tunneling time becomes strongly dependent on the width of the incoming wave packet, which implies that there is no intrinsic tunneling time. This effect is related to the quantum uncertainty in the particle's momentum.

quant-ph↗

arXiv2005

A new way of defining unstable states

We define a new unstable state in the Friedrichs model of a two-level atom. This unstable state is a complex eigenstate of the time evolution operator $\exp(-iHt)$ with a restricted test function space, which is obtained from causality conditions. The unstable state shows exact exponential decay for $t\ge0$. Its emitted field is confined inside the future light-cone. In this way the long-standing problem of exponential catastrophe is removed. This is an example of quantum mechanics outside Hilbert space, which consists of generalized eigenstates in a distribution space, and a dual (test function) space.

physics.atom-ph↗

arXiv2005

Bound states in continuum in an electron waveguide

It is shown that in a double-cavity, two-dimensional electron waveguide, the interplay between quasi-bound states of each cavity leads to the appearance of bound states in continuum for certain distances between the cavities. These bound states may be used to trap electrons in de-localized states distributed in both cavities.

quant-ph↗

arXiv2004

Complex collective states in a one-dimensional two-atom system

We consider a pair of identical two-level atoms interacting with a scalar field in one dimension, separated by a distance $x_{21}$. We restrict our attention to states where one atom is excited and the other is in the ground state, in symmetric or anti-symmetric combinations. We obtain exact collective decaying states, belonging to a complex spectral representation of the Hamiltonian. The imaginary parts of the eigenvalues give the decay rates, and the real parts give the average energy of the collective states. In one dimension there is strong interference between the fields emitted by the atoms, leading to long-range cooperative effects. The decay rates and the energy oscillate with the distance $x_{21}$. Depending on $x_{21}$, the decay rates will either decrease, vanish or increase as compared with the one-atom decay rate. We have sub- and super-radiance at periodic intervals. Our model may be used to study two-cavity electron wave-guides. The vanishing of the collective decay rates then suggests the possibility of obtaining stable configurations, where an electron is trapped inside the two cavities.

quant-ph↗

arXiv2003

Star-unitary transformations. From dynamics to irreversibility and stochastic behavior

We consider a simple model of a classical harmonic oscillator coupled to a field. In standard approaches Langevin-type equations for {\it bare} particles are derived from Hamiltonian dynamics. These equations contain memory terms and are time-reversal invariant. In contrast the phenomenological Langevin equations have no memory terms (they are Markovian equations) and give a time evolution split in two branches (semigroups), each of which breaks time symmetry. A standard approach to bridge dynamics with phenomenology is to consider the Markovian approximation of the former. In this paper we present a formulation in terms of {\it dressed} particles, which gives exact Markovian equations. We formulate dressed particles for Poincaré nonintegrable systems, through an invertible transformation operator $\Lam$ introduced by Prigogine and collaborators. $\Lam$ is obtained by an extension of the canonical (unitary) transformation operator $U$ that eliminates interactions for integrable systems. Our extension is based on the removal of divergences due to Poincaré resonances, which breaks time-symmetry. The unitarity of $U$ is extended to ``star-unitarity'' for $\Lam$. We show that $\Lam$-transformed variables have the same time evolution as stochastic variables obeying Langevin equations, and that $\Lam$-transformed distribution functions satisfy exact Fokker-Planck equations. The effects of Gaussian white noise are obtained by the non-distributive property of $\Lam$ with respect to products of dynamical variables. Therefore our method leads to a direct link between dynamics of Poincaré nonintegrable systems, probability and stochasticity.

cond-mat.stat-mech↗