25 research outputs found
Quantum Stochastic Absorption
We report a detailed and systematic study of wave propagation through a
stochastic absorbing random medium. Stochastic absorption is modeled by
introducing an attenuation constant per unit length in the free
propagation region of the one-dimensional disordered chain of delta function
scatterers. The average value of the logarithm of transmission coefficient
decreases linearly with the length of the sample. The localization length is
given by , where and
are the localization lengths in the presence of only disorder and
of only absorption respectively. Absorption does not introduce any additional
reflection in the limit of large , i.e., reflection shows a monotonic
decrease with and tends to zero in the limit of , in
contrast to the behavior observed in case of coherent absorption. The
stationary distribution of reflection coefficient agrees well with the
analytical results obtained within random phase approximation (RPA) in a larger
parameter space. We also emphasize the major differences between the results of
stochastic and coherent absorption.Comment: RevTex, 6 pages,2 column format, 9 .eps figures include
Dephasing of Aharonov-Bohm oscillations in a mesoscopic ring with a magnetic impurity
We present a detailed analysis of the Aharonov-Bohm interference oscillations
manifested through transmission of an electron in a mesoscopic ring with a
magnetic impurity atom inserted in one of its arms. The electron interacts with
the impurity through the exchange interaction leading to exchange spin-flip
scattering. Transmission in the spin-flipped and spin-unflipped channels are
explicitly calculated. We show that the spin-flipper acts as a dephasor in
spite of absence of any inelastic scattering. The spin-conductance (related to
spin-polarized transmission coefficient) is asymmetric in the flux reversal as
opposed to the two probe conductance which is symmetric under flux reversal.Comment: 4 pages RevTex, 6 figures, brief repor
Modelling of Stochastic Absorption in a Random Medium
We report a detailed and systematic study of wave propagation through a
stochastic absorbing random medium. Stochastic absorption is modeled by
introducing an attenuation constant per unit length in the free
propagation region of the one-dimensional disordered chain of delta function
scatterers. The average value of the logarithm of transmission coefficient
decreases linearly with the length of the sample. The localization length is
given by , where and
are the localization lengths in the presence of only disorder and
of only absorption respectively. Absorption does not introduce any additional
reflection in the limit of large , i.e., reflection shows a monotonic
decrease with and tends to zero in the limit of , in
contrast to the behavior observed in case of coherent absorption. The
stationary distribution of reflection coefficient agrees well with the
analytical results obtained within random phase approximation (RPA) in a larger
parameter space. We also emphasize the major differences between the results of
stochastic and coherent absorption.Comment: 7 pages RevTex, 9 eps figures included, modified version of
cond-mat/9909327, to appear in PRB, mpeg simulations at
http://www.iopb.res.in/~joshi/mpg.htm
Loss of interference in an Aharonov-Bohm ring
We study a simple model of dephasing of Aharonov-Bohm oscillations in the
transmission of an electron across a mesoscopic ring. A magnetic impurity in
one of the arms of the ring couples to the electron spin via an exchange
interaction. This interaction leads to spin flip scattering and induces
dephasing via entanglement. This is akin to the models evoked earlier to
explain destruction of interference due to which-path information in
double-slit experiments. Total transmission is found to be symmetric under flux
reversal but not the spin polarization.Comment: 4 pages, latex/revtex, 4 eps figures. Proceedings of CMDAYS2K, held
at Guru Ghasidas University, Bilaspur, Chattisgarh, India, Aug 29-31, 2
Role of quantum entanglement due to a magnetic impurity on current magnification effect in mesoscopic open rings
We study the current magnification effect in presence of exchange scattering
of electron from a magnetic impurity placed in one arm of an open mesoscopic
ring. The exchange interaction causes entanglement of electron spin and
impurity spin. Earlier studies have shown that such an entanglement causes
reduction or loss of interference in the Aharonov-Bohm oscillations leading to
decoherence. We find however, that this entanglement, in contradiction to the
naive expectation of a reduction of current magnification, leads to enhancement
as well as suppression of the effect. We also observe additional novel features
like new resonances and current reversals.Comment: 5 pages RevTex, 5 figures include
Effect of magnetic flux and of electron momentum on the transmission amplitude in the Aharonov-Bohm ring
A characterization of the two-terminal open-ring Aharonov-Bohm interferometer
is made by analyzing the phase space plots in the complex transmission
amplitude plane. Two types of plots are considered: type I plot which uses the
magnetic flux as the variable parameter and type II plot which uses the
electron momentum as the variable parameter. In type I plot, the trajectory
closes upon itself only when the ratio of the arm lengths (of the
interferometer) is a rational fraction, the shape and the type of the generated
flower-like pattern is sensitive to the electron momentum. For momenta
corresponding to discrete eigenstates of the perfect ring (i.e. the ring
without the leads), the trajectory passes through the origin a certain fixed
number of times before closing upon itself, whereas for arbitrary momenta it
never passes through the origin. Although the transmission coefficient is
periodic in the flux with the elementary flux quantum as the basic period, the
phenomenon of electron transmission is shown not to be so when analyzed via the
present technique. The periodicity is seen to spread over several flux units
whenever is a rational fraction whereas there is absolutely no periodicity
present when is an irrational number. In type II plot, closed trajectories
passing through the origin a number of times are seen for being a rational
fraction. The case R=1 (i.e. a symmetric ring) with zero flux is rather
pathological--it presents a closed loop surrounding the origin. For irrational
values, the trajectories never close.Comment: accepted in Int. J. Mod. Phys. B, RevTeX
A Quantum-Classical Brackets from p-Mechanics
We provide an answer to the long standing problem of mixing quantum and
classical dynamics within a single formalism. The construction is based on
p-mechanical derivation (quant-ph/0212101, quant-ph/0304023) of quantum and
classical dynamics from the representation theory of the Heisenberg group. To
achieve a quantum-classical mixing we take the product of two copies of the
Heisenberg group which represent two different Planck's constants. In
comparison with earlier guesses our answer contains an extra term of analytical
nature, which was not obtained before in purely algebraic setup.
Keywords: Moyal brackets, Poisson brackets, commutator, Heisenberg group,
orbit method, representation theory, Planck's constant, quantum-classical
mixingComment: LaTeX, 7 pages (EPL style), no figures; v2: example of dynamics with
two different Planck's constants is added, minor corrections; v3: major
revion, a complete example of quantum-classic dynamics is given; v4: few
grammatic correction
Mixing quantum and classical mechanics and uniqueness of Planck's constant
Observables of quantum or classical mechanics form algebras called quantum or
classical Hamilton algebras respectively (Grgin E and Petersen A (1974) {\it J
Math Phys} {\bf 15} 764\cite{grginpetersen}, Sahoo D (1977) {\it Pramana} {\bf
8} 545\cite{sahoo}). We show that the tensor-product of two quantum Hamilton
algebras, each characterized by a different Planck's constant is an algebra of
the same type characterized by yet another Planck's constant. The algebraic
structure of mixed quantum and classical systems is then analyzed by taking the
limit of vanishing Planck's constant in one of the component algebras. This
approach provides new insight into failures of various formalisms dealing with
mixed quantum-classical systems. It shows that in the interacting mixed
quantum-classical description, there can be no back-reaction of the quantum
system on the classical. A natural algebraic requirement involving restriction
of the tensor product of two quantum Hamilton algebras to their components
proves that Planck's constant is unique.Comment: revised version accepted for publication in J.Phys.A:Math.Phy
Aharonov-Bohm oscillations and spin transport in a mesoscopic ring with a magnetic impurity
We present a detailed analysis of the Aharonov-Bohm (AB) interference
oscillations manifested through transmission of an electron in a mesoscopic
ring with a magnetic impurity atom inserted in one of its arms. The spin
polarization transport is also studied. The electron interacts with the
impurity through the exchange interaction leading to exchange spin-flip
scattering. Transmission in the spin-flipped and spin-unflipped channels are
explicitly calculated. We show that the entanglement between electron and
spin-flipper states lead to a reduction of AB oscillations in spite of absence
of any inelastic scattering. The spin-conductance (related to spin-polarized
transmission coefficient) is asymmetric in the flux reversal as opposed to the
two probe conductance which is symmetric under flux reversal. We point out
certain limitations of this model in regard to the general notion of dephasing
in quantum mechanics.Comment: 6 pages RevTeX, 9 eps figures included, enlarged version of
cond-mat/000741
Curved space and amorphous structures Part I. Geometric models
This paper offers (in two parts) a broad overview of recent developments concerning the use of curved space concepts in amorphous structures. Keeping particularly in mind nonspecialist readers, expository background material is included, wherever appropriate. Part I deals essentially with geometrical modelling, and starts with a brief recapitualtion of the famous model-building exercise due to Bernal. We then discuss the Kleman-Sadoc prescription for realizing amorphous structures as mappings of spherical polytopes (the four-dimensional analogue of spherical polyhedra) onto Euclidean space. Such an approach has not only provided a fast and convenient algorithm, but more importantly, has focused attention on the line defects (disclinations) in amorphous structures. As a result, one is now able to relate these disclinations to the Frank-Kasper lines present in complex alloy structures. In turn, this has led to a qualitative scenario for the transformation of the liquid during a cool-down, into the crystalline or the amorphous state. Part II deals with attempts to provide a quantitative structure to this scenario via gauge theories