3,215 research outputs found
Semiclassical Diagonalization of Quantum Hamiltonian and Equations of Motion with Berry Phase Corrections
It has been recently found that the equations of motion of several
semiclassical systems must take into account terms arising from Berry phases
contributions. Those terms are responsible for the spin Hall effect in
semiconductor as well as the Magnus effect of light propagating in
inhomogeneous media. Intensive ongoing research on this subject seems to
indicate that a broad class of quantum systems may be affected by Berry phase
terms. It is therefore important to find a general procedure allowing for the
determination of semiclassical Hamiltonian with Berry Phase corrections. This
article presents a general diagonalization method at order for a large
class of quantum Hamiltonians directly inducing Berry phase corrections. As a
consequence, Berry phase terms on both coordinates and momentum operators
naturally arise during the diagonalization procedure. This leads to new
equations of motion for a wide class of semiclassical system. As physical
applications we consider here a Dirac particle in an electromagnetic or static
gravitational field, and the propagation of a Bloch electrons in an external
electromagnetic field.Comment: 15 page
Localization of Sound Sources in a Room with One Microphone
Estimation of the location of sound sources is usually done using microphone
arrays. Such settings provide an environment where we know the difference
between the received signals among different microphones in the terms of phase
or attenuation, which enables localization of the sound sources. In our
solution we exploit the properties of the room transfer function in order to
localize a sound source inside a room with only one microphone. The shape of
the room and the position of the microphone are assumed to be known. The design
guidelines and limitations of the sensing matrix are given. Implementation is
based on the sparsity in the terms of voxels in a room that are occupied by a
source. What is especially interesting about our solution is that we provide
localization of the sound sources not only in the horizontal plane, but in the
terms of the 3D coordinates inside the room
Berry Phase Effects in the dynamics of Dirac Electrons in Doubly Special Relativity Framework
We consider the Doubly Special Relativity (DSR) generalization of Dirac
equation in an external potential in the Magueijo-Smolin base. The particles
obey a modified energy-momentum dispersion relation. The semiclassical
diagonalization of the Dirac Hamiltonian reveals the intrinsic Berry phase
effects in the particle dynamics
Nonadiabatic bounce and an inflationary phase in the quantum mixmaster universe
Following our previous paper, Bergeron et al, Smooth quantum dynamics of the
mixmaster universe, Phys. Rev. D 92, 061302(R) (2015), concerning the
quantization of the vacuum Bianchi IX model and the Born-Huang-Oppenheimer
framework, we present a further analysis of the dynamical properties of the
model. Consistently with the deep quantum regime, we implement the harmonic
approximation of the anisotropy potential. We thus obtain manageable dynamical
equations. We study the quantum anisotropic oscillations during the bouncing
phase of the universe. Neglecting the backreaction from transitions between
quantum anisotropy states we obtain analytical results. In particular, we
identify a parameter which is associated with dynamical properties of the
quantum model and describes a sort of phase transition. Once the parameter
exceeds its critical value, the Born-Huang-Oppenheimer approximation breaks
down. The application of the present result to a simple model of the Universe
indicates that the parameter indeed exceeds its critical value and that there
takes place a huge production of anisotropy at the bounce. This in turn must
lead to a sustained phase of accelerated expansion, an inflationary phase. The
quantitative inclusion of backreaction shall be examined in a follow-up paper
based on the vibronic approach.Comment: 32 pages, 9 figure
- …