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ABSTRACT: The coupling of a mesoscopic system with its environment usually causes total
decoherence: at long times the reduced density matrix of the system evolves in
time to a limit which is independent of its initial value, losing all the
quantum information stored in its initial state. Under special circumstances, a
subspace of the system's Hilbert space remains coherent, or "decoherence free",
and the reduced density matrix approaches a non-trivial limit which contains
information on its initial quantum state, despite the coupling to the
environment. This situation is called "partial decoherence". Here we find the
conditions for partial decoherence for a mesoscopic system (with $N$ quantum
states) which is coupled to an environment. When the Hamiltonian of the system
commutes with the total Hamiltonian, one has "adiabatic decoherence", which
yields N-1 time-independent combinations of the reduced density matrix
elements. In the presence of a magnetic flux, one can measure circulating
currents around loops in the system even at long times, and use them to
retrieve information on the initial state. For N=2, we demonstrate that partial
decoherence can happen only under adiabatic decoherence conditions. However,
for $N>2$ we find partial decoherence even when the Hamiltonian of the system
does not commute with the total Hamiltonian, and we obtain the general
conditions for such non-adiabatic partial decoherence. For an electron moving
on a ring, with $N>2$ single-level quantum dots, non-adiabatic partial
decoherence can arise only when the total flux through the ring vanishes (or
equals an integer number of flux quanta), and therefore there is no asymptotic
circulating current.
05/2012;
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ABSTRACT: We revisit the Anderson-Hasegawa double-exchange model and critically examine its exact solution when the core spins are treated
quantum mechanically. We show that the quantum effects, in the presence of an additional superexchange interaction between
the core spins, yield a term, the significance of which has been hitherto ignored. The importance of this term is further
assessed by numerically exact computation for a four-spin system.
Pramana 04/2012; 61(3):601-609. · 0.57 Impact Factor
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ABSTRACT: This review deals with the dynamics of quantum systems that are subject to high frequency external perturbations. Though the
problem may look hopelessly time-dependent, and poised on the extreme opposite side of adiabaticity, there exists a ‘Kapitza
Window’ over which the dynamics can be treated in terms of effective time-independent Hamiltonians. The consequent results
are important in the context of atomic traps as well as quantum optic properties of atoms in intense and high-frequency electromagnetic
fields.
Pramana 04/2012; 70(3):381-398. · 0.57 Impact Factor
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Sushanta Dattagupta
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ABSTRACT: We present an ‘overview’ of coherence-to-decoherence transition in certain selected problems of condensed matter physics.
Our treatment is based on a subsystem-plus-environment approach. All the examples chosen in this paper have one thing in common
— the environmental degrees of freedom are taken to be bosonic and their spectral density of excitations is assumed to be
‘ohmic’. The examples are drawn from a variety of phenomena in condensed matter physics involving, for instance, quantum diffusion
of hydrogen in metals, Landau diamagnetism and c-axis transport in high T
c superconductors.
Pramana 04/2012; 59(2):203-219. · 0.57 Impact Factor
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ABSTRACT: We consider a prototypical system of an infinite range transverse field Ising
model coupled to a bosonic bath. By integrating out the bosonic degrees, an
effective anisotropic Heisenberg model is obtained for the spin system. The
phase diagram of the latter is calculated as a function of coupling to the heat
bath and the transverse magnetic field. Collective excitations at low
temeratures are assessed within a spin-wave like analysis that exhibits a
vanishing energy gap at the quantum critical point. We also consider another
limit where the system reduces to a generalized spin-boson model of two
interacting spins. By increasing the coupling strength with the heat bath, the
two-spin wavefunction changes from an entangled state to a factorized state of
two spins which are aligned along the transverse field. We also discuss the
possible realization and application of the model to different physical
systems.
04/2011;
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ABSTRACT: The qubit (or a system of two quantum dots) has become a standard paradigm
for studying quantum information processes. Our focus is Decoherence due to
interaction of the qubit with its environment, leading to noise. We consider
quantum noise generated by a dissipative quantum bath. A detailed comparative
study with the results for a classical noise source such as generated by a
telegraph process, enables us to set limits on the applicability of this
process vis a vis its quantum counterpart, as well as lend handle on the
parameters that can be tuned for analyzing decoherence. Both Ohmic and
non-Ohmic dissipations are treated and appropriate limits are analyzed for
facilitating comparison with the telegraph process.
03/2011;
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ABSTRACT: In this Brief Report we show how the low-temperature thermodynamics of the dissipative motion of an electron in a magnetic field is sensitive to the nature of the spectral density function, J(omega), of the quantum heat bath. In all cases of couplings considered here the free energy and the entropy of the cyclotron motion of the electron fall off to zero as power law in conformity with the third law of thermodynamics. The power of the power law however depends on the nature of J(omega). We also separately discuss the influence of confinement.
Physical Review E 04/2010; 81(4 Pt 1):042102. · 2.26 Impact Factor
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ABSTRACT: A qubit (containing two quantum states, 1 and 2), is coupled to a control register (state 3), which is subject to telegraph noise. We study the time evolution of the density matrix $\rho$ of an electron which starts in some coherent state on the qubit. At infinite time, $\rho$ usually approaches the fully decoherent state, with $\rho^{}_{nm}=\delta^{}_{nm}/3$. However, when the Hamiltonian is symmetric under $1\leftrightarrow 2$, the element $\rho^{}_{12}$ approaches a non-zero real value, implying a partial coherence of the asymptotic state. The asymptotic density matrix depends only on ${\rm Re}[\rho^{}_{12}(t=0)]$. In several cases, the information stored on the qubit is protected from the noise. Comment: 4 pages, 2 figures
08/2009;
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ABSTRACT: In this work, low temperature thermodynamic behaviour in the context of dissipative diamagnetism with anomalous coupling is analyzed. We find that finite dissipation substitutes the zero-coupling result of exponential decay of entropy by a power law behaviour at low temperature. For Ohmic bath, entropy vanishes linearly with temperature, $T$, in conformity with Nernst's theorem. It is also shown that entropy decays faster in the presence of anomalous coupling than that of the usual coordinate-coordinate coupling. It is observed that velocity-velocity coupling is the most advantageous coupling scheme to ensure the third law of thermodynamics. It is also revealed that different thermodynamic functions are independent of magnetic field at very low temperature for various coupling schemes discussed in this work.
04/2009;
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ABSTRACT: We revisit here the effect of quantum dissipation on the much studied problem of Landau diamagnetism and analyze the results in the light of the third law of thermodynamics. The case of an additional parabolic potential is separately assessed. We find that dissipation arising from strong coupling of the system to its environment qualitatively alters the low-temperature thermodynamic attributes such as the entropy and the specific heat.
Physical Review E 03/2009; 79(2 Pt 1):021130. · 2.26 Impact Factor
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ABSTRACT: The slow dynamics and concomitant memory (aging) effects seen in nanomagnetic systems are analyzed on the basis of two separate paradigms : superparamagnets and spinglasses. It is argued that in a large class of aging phenomena it suffices to invoke superparamagnetic relaxation of individual single domain particles but with a distribution of their sizes. Cases in which interactions and randomness are important in view of distinctive experimental signatures, are also discussed. Comment: 11 pages and 19 figures
06/2006;
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ABSTRACT: We study the long-time behavior of an underdamped Brownian particle moving through a viscous medium and in a systematic potential, when it is subjected to a space-dependent high-frequency periodic force. When the frequency is very large, much larger than all other relevant system-frequencies, there is a Kapitsa time window wherein the effect of frequency-dependent forcing can be replaced by a static effective potential. Our analysis includes the case in which the forcing, in addition to being frequency-dependent, is space-dependent as well. The results of our analysis then lead to additional contributions to the effective potential. These are applied to the numerical calculation of the diffusion coefficient (D) for a Brownian particle moving in a periodic potential. Presented are numerical results, which are in excellent agreement with theoretical predictions and which indicate a significant enhancement of D due to the space-dependent forcing terms. In addition, we study the transport property (current) of an underdamped Brownian particle in a ratchet potential.
Physical Review E 06/2006; 73(5 Pt 1):051108. · 2.26 Impact Factor
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ABSTRACT: Starting from a quantum Langevin equation (QLE) of a charged particle coupled to a heat bath in the presence of an external magnetic field, we present a fully dynamical calculation of the susceptibility tensor. We further evaluate the position autocorrelation function by using the Gibbs ensemble approach. This quantity is shown to be related to the imaginary part of the dynamical susceptibility, thereby validating the fluctuation-dissipation theorem in the context of dissipative diamagnetism. Finally we present an overview of coherence-to-decoherence transition in the realm of dissipative diamagnetism at zero temperature. The analysis underscores the importance of the details of the relevant physical quantity, as far as coherence to decoherence transition is concerned. Comment: 8 pages and 5 figures
05/2006;
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ABSTRACT: Using the path integral approach to equilibrium statistical physics the effect of dissipation on Landau diamagnetism is calculated. The calculation clarifies the essential role of the boundary of the container in which the electrons move. Further, the derived result for diamagnetization also matches with the expression obtained from a time-dependent quantum Langevin equation in the asymptotic limit, provided a certain order is maintained in taking limits. This identification then unifies equilibrium and nonequilibrium statistical physics for a phenomenon like diamagnetism, which is inherently quantum and strongly dependent on boundary effects. Comment: 4 pages, no figures
04/2005;
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ABSTRACT: An exact treatment of the Anderson - Hasegawa two - site model, incorporating the presence of superexchange and polarons, is used to compute the heat capacity. The calculated results point to the dominance of the lattice contribution, especially in the ferromagnetic regime. This behavior is in qualitative agreement with experimental findings. Comment: 9 pages, Revtex, 4 postscript figures
01/2003;
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ABSTRACT: We revisit the Anderson-Hasegawa double-exchange model and critically examine its exact solution when the core spins are treated quantum mechanically.We show that the quantum effects, in the presence of an additional superexchange interaction between the core spins, yield a term, the significance of which has been hitherto ignored. The quantum considerations further lead to new results when polaronic effects, believed to be ubiquitous in manganites due to electron-phonon coupling, are included. The consequence of these results for the magnetic phase diagrams and the thermal heat capacity is also carefully analysed.
05/2002;
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ABSTRACT: The slow dynamics and concomitant memory (aging) effects seen in nanomagnetic systems are analyzed on the basis of two separate paradigms: superparamagnets and spin glasses. It is argued that in a large class of aging phenomena it suffices to invoke superparamagnetic relaxation of individual single domain particles but with a distribution of their sizes. Cases in which interactions and randomness are important in view of distinctive experimental signatures are also discussed.
Phys. Rev. B. 74(21).
