Coordinación de Física USB

Salón de clases





Grupos de Investigación

Teoría de campos y óptica

Relatividad y campos

Sud-american Network in Quantum Gravity

Sistemas desordenados




JS en Sinai

JS en Orcid



Seminario de Relatividad y Campos

Coloquio de Física




Jorge Stephany: Research

Local density of states in 2DES
Phase space interference and HusimiŽs function
Squeezed number states
Non-abelian Born Infeld actions
Spin Operators and path integrals
Unruh effect
Radiation from moving mirrors


Local density of states in 2DES

Markus Morgenstern, Rudolf Römer and Jorge Stephany

The potential landscape for a 2D disordered electron system obtained by depositing Fe atoms on the InAs(110) surface has been determined experimentally [1]. We use this potential as the input to compute the local density of states of this system by a direct diagonalization of the associated Anderson localization hamiltonian using a modified Lanczos algorithm. The result is then compared with the experimental local density of states obtained by scanning tunneling spectroscopy. We next perform the corresponding computation for the case in which an external magnetic field is applied where Landau quantization has been recently observed[2].

M.Morgenstern et al, Phys. Rev. Lett., 89, (2002) 136806
M.Morgenstern et al, Phys. Rev. Lett., 90}, (2003) 056804

Phase space interference and HusimiŽs function

Douglas Mundarain and Jorge Stephany

The concept of interference in phase space proposed by Wheeler and Schleich some time ago [Nature 326, 574 (1987)] provides an interesting tool to investigate the properties of quantum systems. The validity of the overlapping areas hypothesis has been demonstrated within the WKB approximation but in principle it is not restricted to this approximation. Also relevant is the relation of phase space interference with various the phase space distributions including Husimi Q function.

In Phase space interference and the WKB approximation for squeezed number states. Squeezed number states for a single mode Hamiltonian are investigated from two complementary points of view. Firstly the more relevant features of their photon distribution are discussed using the WKB wave functions. In particular the oscillations of the distribution and the parity behavior are derived and compared with the exact results. The accuracy of the approximation is verified and it is shown that for high photon number it fails to reproduce the true distribution. This is contrasted with the fact that for moderate squeezing the WKB approximation gives the analytical justification to the interpretation of the oscillations as the result of the interference of areas with definite phases in phase space. It is shown with a computation at high squeezing using a modified prescription for the phase space representation which is based on Wigner-Cohen distributions that the failure of the WKB approximation does not invalidate the area overlap picture.

In Husimi's Q function and quantum interference in phase space we discuss a phase space description of the photon number distribution of non classical states which is based on Husimi's Q function and does not rely in the WKB approximation. We illustrate this approach using the examples of displaced number states and two photon coherent states and show it to provide an efficient method for computing and interpreting the photon number distribution . This result is interesting in particular for the two photon coherent states which, for high squeezing, have the probabilities of even and odd photon numbers oscillating independently.

Squeezed number states

Lorenzo Albano, Douglas Mundarain and Jorge Stephany

Squeezed number states of one mode of the electromagnetic field obtained by application of the squeezing operator to the number states and are in principle accessible to experimental study off their properties. In the paper On the squeezed number states and their phase space representations, we compute the photon number distribution, the $Q(\alpha)$ distribution function and the wave functions in the momentum and position representation for a single mode squeezed number state using generating functions which allow to obtain any matrix element in the squeezed number state representation from the matrix elements in the squeezed coherent state representation. For highly squeezed number states we discuss the previously unnoted oscillations which appear in the $Q(\alpha)$ function. We also note that these oscillations can be related to the photon-number distribution oscillations and to the momentum representation of the wave function.

Non Abelian Born Infeld actions

Rita Gianvittorio, Alvaro Restuccia and Jorge Stephany

We introduce a realization of the algebra of diffeomorfisms in terms of the fields of a non-abelian Born-Infeld theory. We construct the Hamiltonian of this theory, describing the interaction of N D-branes. We explicitly obtain the interacting terms to the sixth order in the curvature of the Yang-Mills fields. Our results agree with the ones obtained from interacting string theory which have been done to the fourth order in the curvature.

Spin observables and path integrals

Jose A.López and Jorge Stephany

We are interested in the the formulation of spin observables associated to relativistic and non-relativistic spinning particles in terms of grassmanian differential operators. We use as configuration space variables for the pseudo-classical description of this system the positions $x$ and adequate set of Grassmanian degrees of freedom. We have to consider consider an explicit discretization procedure to obtain the quantum amplitudes as path integrals in this superspace. We compute the quantum action necessary for this description including an explicit expression for the boundary terms. This can be applied to shown how for simple examples, the path integral may be performed in the semi-classical approximation, leading to the correct quantum propagator.

Unruh effect, Rindler photons and classical radiation

Danilo Díaz and Jorge Stephany

In Rindler photons and classical radiation, we describe the quantum and classical radiation emitted by an uniformly accelerating point source in terms of the elementary processes of absorption and emission of Rindler scalar photons of the Fulling-Davies-Unruh bath observed by a co-accelerating observer. To this end we compute the rate at which a DeWitt detector emits a Minkowski scalar particle with defined transverse momentum per unit of proper time of the source and we show that it corresponds to the induced absorption or spontaneous and induced emission of Rindler particles from the thermal bath. We then take what could be called the inert limit of the DeWitt detector by considering the limit of zero gap energy. As suggested by DeWitt, we identify in this limit the detector with a classical point source and verify the consistency of our computation with the classical result. Finally, we study the behavior of the emission rate in D space-time dimensions in connection with the so called apparent statistics inversion.

InRadiative processes of the DeWitt-Takagi detector. we examine the excitation of a uniformly accelerated DeWitt-Takagi detector coupled quadratically to a Majorana-Dirac field. We obtain the transition probability from the ground state of the detector and the vacuum state of the field to an excited state with the emission of a Minkowski pair of quanta, in terms of elementary processes of absorption and scattering of Rindler quanta from the Fulling-Davies-Unruh thermal bath in the co-accelerated frame.

Radiation from moving mirrors

Douglas Mundarain and Jorge Stephany

Using the formalism developed by Moore [ G. T. Moore, J. Math. Phys 11, 2679 (1972) ] for the quantization of fields in cavities with moving reflecting boundaries, we compute in the non relativistic approximation the radiation spectrum for the case when one of the walls move a constant velocity and stops instantaneously at time t=0. We show that the emitted light has non classical properties in particular squeezing in the quadratures of the field.