404 research outputs found
Hydrodynamics, particle relabelling and relativity
Using the wave equation as an example, it is shown how to extend the
hydrodynamic Lagrangian-picture method of constructing field evolution using a
continuum of trajectories to second-order theories. The wave equation is
represented through Eulerian-picture models that are distinguished by their
Lorentz transformation properties. Introducing the idea of the relativity of
the particle label, it is demonstrated how the corresponding trajectory models
are compatible with the relativity principle. It is also shown how the Eulerian
variational formulation may be obtained by canonical transformation from the
Lagrangian picture, and how symmetries in the Lagrangian picture may be used to
generate Eulerian conserved charges.Comment: 21 page
Role of hydrology in development of a vernal clear water phase in an urban impoundment
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72334/1/j.1365-2427.2007.01808.x.pd
Quantum limits on phase-shift detection using multimode interferometers
Fundamental phase-shift detection properties of optical multimode
interferometers are analyzed. Limits on perfectly distinguishable phase shifts
are derived for general quantum states of a given average energy. In contrast
to earlier work, the limits are found to be independent of the number of
interfering modes. However, the reported bounds are consistent with the
Heisenberg limit. A short discussion on the concept of well-defined relative
phase is also included.Comment: 6 pages, 3 figures, REVTeX, uses epsf.st
Quantum trajectory perspective of atom-field interaction in attosecond time scale
Here the ionization and high harmonic generation in Hydrogen and Helium by
using quantum (hydrodynamic) trajectories is analyzed theoretically. The
quantum trajectories allow a self-contained treatment of the electron exchange
and correlation effects without introducing ad hoc potentials into the
Schrodinger equation. Our approach predicts the correct high harmonic spectra
and the attosecond pulses generated by the Helium atom beyond the single active
electron approximation. It can be used to study complex multi-electron systems
and their interaction with laser field of both high and low intensity.Comment: 8 pages, 4 figure
Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories
This paper examines the nature of classical correspondence in the case of
coherent states at the level of quantum trajectories. We first show that for a
harmonic oscillator, the coherent state complex quantum trajectories and the
complex classical trajectories are identical to each other. This congruence in
the complex plane, not restricted to high quantum numbers alone, illustrates
that the harmonic oscillator in a coherent state executes classical motion. The
quantum trajectories are those conceived in a modified de Broglie-Bohm scheme
and we note that identical classical and quantum trajectories for coherent
states are obtained only in the present approach. The study is extended to
Gazeau-Klauder and SUSY quantum mechanics-based coherent states of a particle
in an infinite potential well and that in a symmetric Poschl-Teller (PT)
potential by solving for the trajectories numerically. For the coherent state
of the infinite potential well, almost identical classical and quantum
trajectories are obtained whereas for the PT potential, though classical
trajectories are not regained, a periodic motion results as t --> \infty.Comment: More example
High Order Multistep Methods with Improved Phase-Lag Characteristics for the Integration of the Schr\"odinger Equation
In this work we introduce a new family of twelve-step linear multistep
methods for the integration of the Schr\"odinger equation. The new methods are
constructed by adopting a new methodology which improves the phase lag
characteristics by vanishing both the phase lag function and its first
derivatives at a specific frequency. This results in decreasing the sensitivity
of the integration method on the estimated frequency of the problem. The
efficiency of the new family of methods is proved via error analysis and
numerical applications.Comment: 36 pages, 6 figure
Input-output theory for fermions in an atom cavity
We generalize the quantum optical input-output theory developed for optical
cavities to ultracold fermionic atoms confined in a trapping potential, which
forms an "atom cavity". In order to account for the Pauli exclusion principle,
quantum Langevin equations for all cavity modes are derived. The dissipative
part of these multi-mode Langevin equations includes a coupling between cavity
modes. We also derive a set of boundary conditions for the Fermi field that
relate the output fields to the input fields and the field radiated by the
cavity. Starting from a constant uniform current of fermions incident on one
side of the cavity, we use the boundary conditions to calculate the occupation
numbers and current density for the fermions that are reflected and transmitted
by the cavity
Interference, reduced action, and trajectories
Instead of investigating the interference between two stationary, rectilinear
wave functions in a trajectory representation by examining the two rectilinear
wave functions individually, we examine a dichromatic wave function that is
synthesized from the two interfering wave functions. The physics of
interference is contained in the reduced action for the dichromatic wave
function. As this reduced action is a generator of the motion for the
dichromatic wave function, it determines the dichromatic wave function's
trajectory. The quantum effective mass renders insight into the behavior of the
trajectory. The trajectory in turn renders insight into quantum nonlocality.Comment: 12 pages text, 5 figures. Typos corrected. Author's final submission.
A companion paper to "Welcher Weg? A trajectory representation of a quantum
Young's diffraction experiment", quant-ph/0605121. Keywords: interference,
nonlocality, trajectory representation, entanglement, dwell time, determinis
4f-spin dynamics in La(2-x-y)Sr(x)Nd(y)CuO(4)
We have performed inelastic magnetic neutron scattering experiments on
La(2-x-y)Sr(x)Nd(y)CuO(4) in order to study the Nd 4f-spin dynamics at low
energies. In all samples we find at high temperatures a quasielastic line
(Lorentzian) with a line width which decreases on lowering the temperature. The
temperature dependence of the quasielastic line width Gamma/2(T) can be
explained with an Orbach-process, i.e. a relaxation via the coupling between
crystal field excitations and phonons. At low temperatures the Nd-4f magnetic
response S(Q,omega) correlates with the electronic properties of the
CuO(2)-layers. In the insulator La(2-y)Nd(y)CuO(4) the quasielastic line
vanishes below 80 K and an inelastic excitation occurs. This directly indicates
the splitting of the Nd3+ ground state Kramers doublet due to the static
antiferromagnetic order of the Cu moments. In La(1.7-x)Sr(x)Nd(0.3)CuO(4) with
x = 0.12, 0.15 and La(1.4-x)Sr(x)Nd(0.6)CuO(4) with x = 0.1, 0.12, 0.15, 0.18
superconductivity is strongly suppressed. In these compounds we observe a
temperature independent broad quasielastic line of Gaussian shape below T about
30 K. This suggests a distribution of various internal fields on different Nd
sites and is interpreted in the frame of the stripe model. In
La(1.8-y)Sr(0.2)Nd(y)CuO(4) (y = 0.3, 0.6) such a quasielastic broadening is
not observed even at lowest temperature.Comment: 8 pages, 10 figures included, to appear in Phys. Rev.
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