35,675 research outputs found
Atomic Nuclei with Tetrahedral and Octahedral Symmetries
We present possible manifestations of octahedral and tetrahedral symmetries
in nuclei. These symmetries are associated with the OhD and TdD double point
groups. Both of them have very characteristic finger-prints in terms of the
nucleonic level properties - unique in the Fermionic universe. The tetrahedral
symmetry leads to the four-fold degeneracies in the nucleonic spectra; it does
not preserve the parity. The octahedral symmetry leads to the four-fold
degeneracies in the nucleonic spectra as well but it does preserve the parity.
Microscopic predictions have been obtained using mean-field theory based on
the relativistic equations and confirmed by using 'traditional' Schroedinger
equation formalism. Calculations are performed in multidimensional deformation
spaces using newly designed algorithms.
We discuss some experimental fingerprints of the hypothetical new symmetries
and possibilities of their verification through experiments.Comment: 24 pages, LaTeX, Invited lecture on the XXXVII School of Nuclear
Physics, Zakopane 2002, Polan
Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point
We study an infinite range ferromagnetic Ising model in the presence of a
transverse magnetic field which exhibits a quantum paramagnetic-ferromagnetic
phase transition at a critical value of the transverse field. In the
thermodynamic limit, the low-temperature properties of this model are dominated
by the behavior of a single large classical spin governed by an anisotropic
Hamiltonian. Using this property, we study the quench and AC dynamics of the
model both numerically and analytically, and develop a correspondence between
the classical phase space dynamics of a single spin and the quantum dynamics of
the infinite-range ferromagnetic Ising model. In particular, we compare the
behavior of the equal-time order parameter correlation function both near to
and away from the quantum critical point in the presence of a quench or AC
transverse field. We explicitly demonstrate that a clear signature of the
quantum critical point can be obtained by studying the AC dynamics of the
system even in the classical limit. We discuss possible realizations of our
model in experimental systems.Comment: Revtex4, 10 pages including 10 figures; corrected a sign error in Eq.
32; this is the final published versio
Landau-Zener quantum tunneling in disordered nanomagnets
We study Landau-Zener macroscopic quantum transitions in ferromagnetic metal
nanoparticles containing on the order of 100 atoms. The model that we consider
is described by an effective giant-spin Hamiltonian, with a coupling to a
random transverse magnetic field mimicking the effect of quasiparticle
excitations and structural disorder on the gap structure of the spin collective
modes. We find different types of time evolutions depending on the interplay
between the disorder in the transverse field and the initial conditions of the
system. In the absence of disorder, if the system starts from a low-energy
state, there is one main coherent quantum tunneling event where the
initial-state amplitude is completely depleted in favor of a few discrete
states, with nearby spin quantum numbers; when starting from the highest
excited state, we observe complete inversion of the magnetization through a
peculiar ``backward cascade evolution''. In the random case, the
disorder-averaged transition probability for a low-energy initial state becomes
a smooth distribution, which is nevertheless still sharply peaked around one of
the transitions present in the disorder-free case. On the other hand, the
coherent backward cascade phenomenon turns into a damped cascade with
frustrated magnetic inversion.Comment: 21 pages, 7 figures, to be published in Phys.Rev.
Fermionic SK-models with Hubbard interaction: Magnetism and electronic structure
Models with range-free frustrated Ising spin- and Hubbard interaction are
treated exactly by means of the discrete time slicing method. Critical and
tricritical points, correlations, and the fermion propagator, are derived as a
function of temperature T, chemical potential \mu, Hubbard coupling U, and spin
glass energy J. The phase diagram is obtained. Replica symmetry breaking
(RSB)-effects are evaluated up to four-step order (4RSB). The use of exact
relations together with the 4RSB-solutions allow to model exact solutions by
interpolation. For T=0, our numerical results provide strong evidence that the
exact density of states in the spin glass pseudogap regime obeys \rho(E)=const
|E-E_F| for energies close to the Fermi level. Rapid convergence of \rho'(E_F)
under increasing order of RSB is observed. The leading term resembles the
Efros-Shklovskii Coulomb pseudogap of localized disordered fermionic systems in
2D. Beyond half filling we obtain a quadratic dependence of the fermion filling
factor on the chemical potential. We find a half filling transition between a
phase for U>\mu, where the Fermi level lies inside the Hubbard gap, into a
phase where \mu(>U) is located at the center of the upper spin glass pseudogap
(SG-gap). For \mu>U the Hubbard gap combines with the lower one of two SG-gaps
(phase I), while for \mu<U it joins the sole SG-gap of the half-filling regime
(phase II). We predict scaling behaviour at the continuous half filling
transition. Implications of the half-filling transition between the deeper
insulating phase II and phase I for delocalization due to hopping processes in
itinerant model extensions are discussed and metal-insulator transition
scenarios described.Comment: 29 pages, 26 Figures, 4 jpeg- and 3 gif-Fig-files include
Nuclear Tetrahedral Symmetry: Possibly Present Throughout the Periodic Table
More than half a century after the fundamental, spherical shell structure in
nuclei has been established, theoretical predictions indicate that the
shell-gaps comparable or even stronger than those at spherical shapes may
exist. Group-theoretical analysis supported by realistic mean-field
calculations indicate that the corresponding nuclei are characterized by the
('double-tetrahedral') group of symmetry, exact or approximate. The
corresponding strong shell-gap structure is markedly enhanced by the existence
of the 4-dimensional irreducible representations of the group in question and
consequently it can be seen as a geometrical effect that does not depend on a
particular realization of the mean-field. Possibilities of discovering the
corresponding symmetry in experiment are discussed.Comment: 4 pages in LaTeX and 4 figures in eps forma
Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
We study first-order quantum phase transitions in models where the mean-field
traitment is exact, and the exponentially fast closure of the energy gap with
the system size at the transition. We consider exactly solvable ferromagnetic
models, and show that they reduce to the Grover problem in a particular limit.
We compute the coefficient in the exponential closure of the gap using an
instantonic approach, and discuss the (dire) consequences for quantum
annealing.Comment: 6 pages, 3 figure
Commensurate-Incommensurate Phase Transitions for Multichain Quantum Spin Models: Exact Results
The behavior in an external magnetic field is studied for a wide class of
multichain quantum spin models. It is shown that the magnetic field together
with the interchain couplings cause commensurate-incommensurate phase
transitions between the gapless phases in the ground state. The conformal limit
of these models is studied and it is shown that the low-lying excitations for
the incommensurate phases are not independent. A scenario for the transition
from one to two space dimensions for the integrable multichain models is
proposed. The similarities in the external field behavior for the quantum
multichain spin models and a wide class of quantum field theories are
discussed. The exponents for the gaps caused by relevant perturbations of the
models are calculated.Comment: 23 pages, LaTeX, typos correcte
The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
Among various algorithms designed to exploit the specific properties of
quantum computers with respect to classical ones, the quantum adiabatic
algorithm is a versatile proposition to find the minimal value of an arbitrary
cost function (ground state energy). Random optimization problems provide a
natural testbed to compare its efficiency with that of classical algorithms.
These problems correspond to mean field spin glasses that have been extensively
studied in the classical case. This paper reviews recent analytical works that
extended these studies to incorporate the effect of quantum fluctuations, and
presents also some original results in this direction.Comment: 151 pages, 21 figure
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