6 research outputs found
Lasing Threshold and Mode Competition in Chaotic Cavities
The lasing threshold is studied of a multi-mode chaotic cavity (linear size D
>> wavelength \lambda) coupled to the outside through a small hole (linear size
d << \lambda). For sufficiently weak absorption by the boundaries, the
statistical distribution of the threshold is wide, its mean value being much
less than the pumping rate needed to compensate the average loss. The average
number N_{nc} >> 1 of non-competing excited modes is proportional to the square
root of the pumping rate. We use the classical model of spatial hole burning to
account for mode competition and find a reduction in the average number of
excited modes to N =3^{1/3} N_{nc}^{2/3}.Comment: 6 pages, RevTeX, 3 figures. Discussion of effects of non-zero
resistivity in the boundaries is adde
Mode Repulsion and Mode Coupling in Random Lasers
We studied experimentally and theoretically the interaction of lasing modes
in random media. In a homogeneously broadened gain medium, cross gain
saturation leads to spatial repulsion of lasing modes. In an inhomogeneously
broadened gain medium, mode repulsion occurs in the spectral domain. Some
lasing modes are coupled through photon hopping or electron absorption and
reemission. Under pulsed pumping, weak coupling of two modes leads to
synchronization of their lasing action. Strong coupling of two lasing modes
results in anti-phased oscillations of their intensities.Comment: 13 pages, 4 figure
Topological superfluid He-B: fermion zero modes on interfaces and in the vortex core
Many quantum condensed matter systems are strongly correlated and strongly
interacting fermionic systems, which cannot be treated perturbatively. However,
topology allows us to determine generic features of their fermionic spectrum,
which are robust to perturbation and interaction. We discuss the nodeless 3D
system, such as superfluid He-B, vacuum of Dirac fermions, and relativistic
singlet and triplet supercondutors which may arise in quark matter. The
systems, which have nonzero value of topological invariant, have gapless
fermions on the boundary and in the core of quantized vortices. We discuss the
index theorem which relates fermion zero modes on vortices with the topological
invariants in combined momentum and coordinate space.Comment: paper is prepared for Proceedings of the Workshop on Vortices,
Superfluid Dynamics, and Quantum Turbulence held on 11-16 April 2010, Lammi,
Finlan
Signatures of Classical Diffusion in Quantum Fluctuations of 2D Chaotic Systems
We consider a two-dimensional (2D) generalization of the standard
kicked-rotor (KR) and show that it is an excellent model for the study of 2D
quantum systems with underlying diffusive classical dynamics. First we analyze
the distribution of wavefunction intensities and compare them with the
predictions derived in the framework of diffusive {\it disordered} samples.
Next, we turn the closed system into an open one by constructing a scattering
matrix. The distribution of the resonance widths and Wigner
delay times are investigated. The forms of these
distributions are obtained for different symmetry classes and the traces of
classical diffusive dynamics are identified. Our theoretical arguments are
supported by extensive numerical calculations.Comment: 20 pages; 12 figure
Field quantization for open optical cavities
We study the quantum properties of the electromagnetic field in optical
cavities coupled to an arbitrary number of escape channels. We consider both
inhomogeneous dielectric resonators with a scalar dielectric constant
and cavities defined by mirrors of arbitrary shape. Using
the Feshbach projector technique we quantize the field in terms of a set of
resonator and bath modes. We rigorously show that the field Hamiltonian reduces
to the system--and--bath Hamiltonian of quantum optics. The field dynamics is
investigated using the input--output theory of Gardiner and Collet. In the case
of strong coupling to the external radiation field we find spectrally
overlapping resonator modes. The mode dynamics is coupled due to the damping
and noise inflicted by the external field. For wave chaotic resonators the mode
dynamics is determined by a non--Hermitean random matrix. Upon including an
amplifying medium, our dynamics of open-resonator modes may serve as a starting
point for a quantum theory of random lasing.Comment: 16 pages, added references, corrected typo
Phase Defects and Order Parameter Space for Penrose Tilings
A new invariant classifying phase defects of Penrose tilings is constructed. This invariant takes
values in the group closely related to the fundamental group of a certain topological space, which
is the image of the tiling itself under identifications dictated by matching rules. This space plays
the role of the order parameter space for pentagonal quasicrystals. The invariant enables us to
discriminate between mismatches of different directions