1,721,021 research outputs found
Nonequilibrium transport on a quantum molecular chain in terms of the complex Liouvillian spectrum
Get PDFThe transport process in a molecular chain in a nonequilibrium stationary state is theoretically investigated. The molecule is interacting at both ends with thermal baths of different temperatures, while no dissipation mechanism is contained inside the molecular chain. We have first obtained the nonequilibrium stationary state outside the Hilbert space in terms of the complex spectral representation of Liouvillian. The nonequilibrium stationary state is obtained as an eigenstate of the Liouvillian, which is constructed through the collision invariant of the kinetic equation. The eigenstate of the Liouvillian contains information on the spatial correlation between the molecular chain and the thermal baths. While energy flow in the nonequilibrium state which is due to the first-order correlation can be described by the Landauer formula, the particle current due to the second-order correlation cannot be described by the Landauer formula. The present method provides a simple way to evaluate the energy transport in a molecular chain in a nonequilibrium situation.Ministry of Education, Science, Sports, and Culture of JapanYukawa International Program for Quark-Hadron Sciences YIPQSPhysic
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Coherence and decoherence processes of a harmonic oscillator coupled with finite temperature field: exact eigenbasis solution of Kossakowski-Linblad's equation
Get PDFtextThe eigenvalue problem of Kossakowski-Linblad’s kinetic equation associated
with the reduced density matrix of a harmonic oscillator interacting
with a thermal bath in equilibrium is solved. The solution gives rise to a
complete orthogonal eigenbasis endowed with Hilbert space structure that has
a weighted norm. We find that the eigenfunctions at finite temperature can
be obtained from the eigenfunction at zero temperature through a hyperbolic
rotation on the position variables. This transformation enables the extension
of the simple harmonic oscillator density matrix to that of a finite temperature.
We further investigate the decay of these extended states under our
dissipative kinetic equation. Furthermore, the Hilbert space structure enables
the proof of a H-theorem in this system. We apply the eigenbasis expansion of
an initial state to analyze decohorence as well as coherence processes. We find
that coherence process occurs at a longer time scale compared to decoherence
process. The time scales of both processes are estimated with the eigenbasis
expansion. In the same way we analyze the evolution of the coherent state.
We show that in addition to the ordinary decay time, we found another time
scale which is defined by the time when the motion of the peak of the coherent
state become comparative to the width of the coherent state. In contrast to
the ordinary decay time this new relaxation time depends on the initial value
of the momentum of the oscillator. We also find that our eigenbasis is applicable
to a class of non-linear interactions, with a slight extension of the form
of transport coefficients due to the non-linear interactions.Physic
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Resonance overlap, secular effects and non-integrability: an approach from ensemble theory
No full texttextPhysic
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Suppression of radiation damping in electromagnetic waveguide, signature of quantum decoherence in the field bath
Get PDFtextRecent development of spectral analysis of the Liouville-von Neumann equation
has revealed the fact that irreversibility is a rigorous dynamical property of
Poincaré non-integrable systems with an infinite degrees of freedom interacting
among each other through resonance coupling. In the present work we discuss
this role of resonance in some examples of matter-field coupling systems for both
classical and quantum mechanics: the one is a classical motion of a charged particle
in electromagnetic waveguide, and the other is the decoherence problem of quantum
matter-field interacting systems.
In the first part of this dissertation, we study an accelerated motion of a
charged classical dipole molecule with frequency ω1 inside the rectangular waveguide.
If the particle is in free space, it is well known that its accelerated motion will
eventually stop by radiating the field through the resonance interaction. This result
is the so-called radiation damping. For the case in the waveguide, there are two
possible situations, due to the existence of the cut-off frequency ωc of the waveguide.
Under the cut-off frequency electromagnetic wave cannot propagate inside the
waveguide. The stability of the dipole depends on the relation between ω1 and ωc.
For ω1 < ωc, the dipole cannot resonate with the field. This corresponds to the
Poincaré integrable system. For this case the dipole keeps its accelerated motion
without emitting the radiating field. Therefore the radiation damping of the dipole
molecules is suppressed inside the waveguide under the absence of resonance interaction.
The motion of this steady state somewhat resembles a quantum ground state.
We show that this steady state is dressed by electromagnetic field. The overlap
of the dressing field leads to a force analogous to van der Waals force in quantum
mechanics. The critical frequency determined by ω1 = ωc gives a critical size of the
waveguide. For heavy molecules, such as HCl, this is of order 10−5m. We show that
the size of the dressing field is the same order of the size of the waveguide. Hence
we have a macroscopic size of the dressing in the waveguide.
For ω1 > ωc, the dipole can resonate with the field, and the system becomes
non-integrable in the sense of Poincaré. As a result, the accelerated motion eventually
stop by emitting the resonance field. This corresponds to the problem of
classical radiation damping. We show that there is non-negligible deviation of exponential
decay in a short time scale of the order t ∼ 1/ω1. This corresponds to the
quantum Zeno effect, well known in quantum unstable systems. After this period,
the dipole decays exponentially in time by emitting the resonance field. We found
by choosing ωc very close to ω1, we can increase the decay rate 105
times faster than
the case where the dipole is in the free space, at the same time the emitted field
travel 10−4
times slower than the speed of light. This is again a consequence of the
existence of the cut-off frequency in the waveguide. Indeed, the cut-off frequency
leads to a non-linear dispersion relation for the electromagnetic field. To some extent,
the electromagnetic field is sticky inside the waveguide. Due to the large decay
rate and slower speed of light, the size of the wavepacket emitted by the dipole is
significantly small (about 10cm for HCl). This is even smaller than the quantum
case in free space, where the wavepacket of the field emitted by the decay of electron
in hydrogen atom is about 1m.
In the second part of this dissertation, we study a quantum matter-field
coupled system. We focus our attention on the problem of quantum decoherence in
a system of a particle coupled with a field, the Hamiltonian of which has a similar
structure to the problem of classical radiation damping mentioned above.
We apply the complex spectral representation of the Liouville-von Neumann
operator that gives a rigorous approach to the irreversible processes. We focus
our attention on the time evolution of the field, which is commonly neglected in
phenomenological approaches to the decoherence problem. We found a signature of
decoherence in the field which has a characteristic time dependence proportional to
t that comes from the secular effect between the particle and the field through the
resonance interaction that breaks time-symmetry.Physic
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The role of the Van Hove singularity in the time evolution of electronic states in a low-dimensional superlattice semiconductor
No full texttextOver the last three decades, the rapid development of efficient synthetic routes for
the preparation of expanded porphyrin macrocycles has allowed the exploration of a new
frontier involving “porphyrin-like” coordination chemistry. This doctoral dissertation
describes the author’s exploratory journey into the area of transition metal cation
complexation using oligopyrrolic macrocycles. The reported synthetic findings were used
to gain new insights into the factors affecting the observed coordination modes and to
probe the emerging roles of counter-anion effects, tautomeric equilibria and hydrogenbonding
interactions in regulating the metalation chemistry of expanded porphyrins.
The first chapter provides an updated overview of this relatively young
coordination chemistry subfield and introduces the idea of expanded porphyrins as a
diverse family of ligands for metalation studies. Chapter 2 details the synthesis of a series
of binuclear complexes and illustrates the importance of metal oxidation state,
macrocycle protonation and counter-anion effects in terms of defining the final structure
of the observed metal complexes. The binding study reported in Chapter 3 demonstrates a
strong positive allosteric effect for the coordination of silver(I) cations in a Schiff base
expanded porphyrin. Chapter 4 introduces the use of oligopyrrolic macrocycles for the
stabilization of early transition metal cations. Specifically, the preparation of a series of
vanadium complexes illustrates the bimodal (i.e., covalent and noncovalent) recognition
of the non-spherical dioxovanadium(V) species within the macrocyclic cavities.
Experimental procedures and characterization data are reported in Chapter 5.Physic
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Star-unitary transformation and stochasticity: emergence of white, 1/f noise through resonances
Get PDFIn this thesis we consider the problem of stochasticity in Hamiltonian
dynamics. It was shown by Poincaré that nonintegrable systems do not have
constants of motion due to resonances. Divergences due to resonances appear when we try to solve the Hamiltonian by perturbation. In recent years,
Prigogine’s group showed that there may exist a new way of solving the Hamiltonian by introducing a non-unitary transformation Λ which removes the divergences systematically. In this thesis we apply this Λ transformation to the
problem of stochasticity.
To this end, first we study classical Friedrichs model, which describes
the interaction between a particle and field. For this model we derive the
Λ transformation for general functions of particle modes, and show that the
Langevin and Fokker-Planck equations can be derived through the transformed
particle density function. It is also shown that the Gaussian white noise structure can be derived through the removal of divergences due to resonances. We extend this to the quantum case, and show that the same structure can be
preserved if we keep the normal order of creation and destruction operators.
We also study the extended Friedrichs model. This model can be mapped
from the case in which a small system is weakly interacting with a reservoir.
In this model we show that low frequency 1/f noise is derived due to the sum
of resonances effect.Physic
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Tunable bound-states in continuum by optical frequency
Get PDFtextWe demonstrate the existence of tunable bound-states in continuum (BIC) in a 1-dimensional quantum wire with two impurities by an intense monochromatic radiation field. We found that there is a new type of BIC due to the Fano interference between two optical transition channels, in addition to the ordinary BIC due to a geometrical interference between electron wave functions emitted by impurities. In both cases the BIC can be achieved by tuning the frequency of the radiation field.Physic
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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