10,900 research outputs found
Quantum Resonances and Regularity Islands in Quantum Maps
We study analytically as well as numerically the dynamics of a quantum map
near a quantum resonance of an order q. The map is embedded into a continuous
unitary transformation generated by a time-independent quasi-Hamiltonian. Such
a Hamiltonian generates at the very point of the resonance a local gauge
transformation described the unitary unimodular group SU(q). The resonant
energy growth of is attributed to the zero Liouville eigenmodes of the
generator in the adjoint representation of the group while the non-zero modes
yield saturating with time contribution. In a vicinity of a given resonance,
the quasi-Hamiltonian is then found in the form of power expansion with respect
to the detuning from the resonance. The problem is related in this way to the
motion along a circle in a (q^2-1)-component inhomogeneous "magnetic" field of
a quantum particle with intrinsic degrees of freedom described by the SU(q)
group. This motion is in parallel with the classical phase oscillations near a
non-linear resonance. The most important role is played by the resonances with
the orders much smaller than the typical localization length, q << l. Such
resonances master for exponentially long though finite times the motion in some
domains around them. Explicit analytical solution is possible for a few lowest
and strongest resonances.Comment: 28 pages (LaTeX), 11 ps figures, submitted to PR
Nonlocal density functionals and the linear response of the homogeneous electron gas
The known and usable truly nonlocal functionals for exchange-correlation
energy of the inhomogeneous electron gas are the ADA (average density
approximation) and the WDA (weighted density approximation). ADA, by design,
yields the correct linear response function of the uniform electron gas. WDA is
constructed so that it is exact in the limit of one-electron systems. We derive
an expression for the linear response of the uniform gas in the WDA, and
calculate it for several flavors of WDA. We then compare the results with the
Monte-Carlo data on the exchange-correlation local field correction, and
identify the weak points of conventional WDA in the homogeneous limit. We
suggest how the WDA can be modified to improve the response function. The
resulting approximation is a good one in both opposite limits, and should be
useful for practical nonlocal density functional calculations.Comment: 4 pages, two eps figures embedde
Solutions of the dispersion equation in the region of overlapping of zero-sound and particle-hole modes
In this paper the solutions of the zero-sound dispersion equation in the
random phase approximation (RPA) are considered. The calculation of the damped
zero-sound modes \omega_s(k) (complex frequency of excitation) in the nuclear
matter is presented. The method is based on the analytical structure of the
polarization operators \Pi(\omega,k). The solutions of two dispersion equations
with \Pi(\omega,k) and with Re(\Pi(\omega,k)) are compared. It is shown that in
the first case we obtain one-valued smooth solutions without "thumb-like"
forms. Considering the giant resonances in the nuclei as zero-sound excitations
we compare the experimental energy and escape width of the giant dipole
resonance (GDR) in the nucleus A with \omega_s(k) taken at a definite wave
vector k=k_A.Comment: 14 pages, 5 figures; revised versio
Quantum Resonances of Kicked Rotor and SU(q) group
The quantum kicked rotor (QKR) map is embedded into a continuous unitary
transformation generated by a time-independent quasi-Hamiltonian. In some
vicinity of a quantum resonance of order , we relate the problem to the {\it
regular} motion along a circle in a -component inhomogeneous
"magnetic" field of a quantum particle with intrinsic degrees of freedom
described by the group. This motion is in parallel with the classical
phase oscillations near a non-linear resonance.Comment: RevTeX, 4 pages, 3 figure
Action scales for quantum decoherence and their relation to structures in phase space
A characteristic action is defined whose magnitude determines some
properties of the expectation value of a general quantum displacement operator.
These properties are related to the capability of a given environmental
`monitoring' system to induce decoherence in quantum systems coupled to it. We
show that the scale for effective decoherence is given by . We relate this characteristic action with a complementary
quantity, , and analyse their connection with the main features of
the pattern of structures developed by the environmental state in different
phase space representations. The relevance of the -action scale is
illustrated using both a model quantum system solved numerically and a set of
model quantum systems for which analytical expressions for the time-averaged
expectation value of the displacement operator are obtained explicitly.Comment: 12 pages, 3 figure
A dissymmetric [Gd2] coordination molecular dimer hosting six addressable spin qubits
Artificial magnetic molecules can host several spin qubits, which could then implement small-scale algorithms. In order to become of practical use, such molecular spin processors need to increase the available computational space and warrant universal operations. Here, we design, synthesize and fully characterize dissymetric molecular dimers hosting either one or two Gadolinium(III) ions. The strong sensitivity of Gadolinium magnetic anisotropy to its local coordination gives rise to different zero-field splittings at each metal site. As a result, the [LaGd] and [GdLu] complexes provide realizations of distinct spin qudits with eight unequally spaced levels. In the [Gd2] dimer, these properties are combined with a Gd-Gd magnetic interaction, sufficiently strong to lift all level degeneracies, yet sufficiently weak to keep all levels within an experimentally accessible energy window. The spin Hamiltonian of this dimer allows a complete set of operations to act as a 64-dimensional all-electron spin qudit, or, equivalently, as six addressable qubits. Electron paramagnetic resonance experiments show that resonant transitions between different spin states can be coherently controlled, with coherence times TM of the order of 1 µs limited by hyperfine interactions. Coordination complexes with embedded quantum functionalities are promising building blocks for quantum computation and simulation hybrid platforms
Hierarchy of QM SUSYs on a Bounded Domain
We systematically formulate a hierarchy of isospectral Hamiltonians in
one-dimensional supersymmetric quantum mechanics on an interval and on a
circle, in which two successive Hamiltonians form N=2 supersymmetry. We find
that boundary conditions compatible with supersymmetry are severely restricted.
In the case of an interval, a hierarchy of, at most, three isospectral
Hamiltonians is possible with unique boundary conditions, while in the case of
a circle an infinite tower of isospectral Hamiltonians can be constructed with
two-parameter family of boundary conditions.Comment: 15 pages, 3 figure
Heat conduction in one dimensional systems: Fourier law, chaos, and heat control
In this paper we give a brief review of the relation between microscopic
dynamical properties and the Fourier law of heat conduction as well as the
connection between anomalous conduction and anomalous diffusion. We then
discuss the possibility to control the heat flow.Comment: 15 pages, 11 figures. To be published in the Proceedings of the NATO
Advanced Research Workshop on Nonlinear Dynamics and Fundamental
Interactions, Tashkent, Uzbekistan, Octo. 11-16, 200
Arbitrary Choice of Basic Variables in Density Functional Theory. II. Illustrative Applications
Our recent theory (Ref. 1) enables us to choose arbitrary quantities as the
basic variables of the density functional theory. In this paper we apply it to
several cases. In the case where the occupation matrix of localized orbitals is
chosen as a basic variable, we can obtain the single-particle equation which is
equivalent to that of the LDA+U method. The theory also leads to the
Hartree-Fock-Kohn-Sham equation by letting the exchange energy be a basic
variable. Furthermore, if the quantity associated with the density of states
near the Fermi level is chosen as a basic variable, the resulting
single-particle equation includes the additional potential which could mainly
modify the energy-band structures near the Fermi level.Comment: 27 page
Impurity effects on the melting of Ni clusters
We demonstrate that the addition of a single carbon impurity leads to
significant changes in the thermodynamic properties of Ni clusters consisting
of more than a hundred atoms. The magnitude of the change induced is dependent
upon the parameters of the Ni-C interaction. Hence, thermodynamic properties of
Ni clusters can be effectively tuned by the addition of an impurity of a
particular type. We also show that the presence of a carbon impurity
considerably changes the mobility and diffusion of atoms in the Ni cluster at
temperatures close to its melting point. The calculated diffusion coefficients
of the carbon impurity in the Ni cluster can be used for a reliable estimate of
the growth rate of carbon nanotubes.Comment: 27 pages, 13 figure
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