5,017 research outputs found
The fundamental limit on the rate of quantum dynamics: the unified bound is tight
The question of how fast a quantum state can evolve has attracted a
considerable attention in connection with quantum measurement, metrology, and
information processing. Since only orthogonal states can be unambiguously
distinguished, a transition from a state to an orthogonal one can be taken as
the elementary step of a computational process. Therefore, such a transition
can be interpreted as the operation of "flipping a qubit", and the number of
orthogonal states visited by the system per unit time can be viewed as the
maximum rate of operation.
A lower bound on the orthogonalization time, based on the energy spread
DeltaE, was found by Mandelstam and Tamm. Another bound, based on the average
energy E, was established by Margolus and Levitin. The bounds coincide, and can
be exactly attained by certain initial states if DeltaE=E; however, the problem
remained open of what the situation is otherwise.
Here we consider the unified bound that takes into account both DeltaE and E.
We prove that there exist no initial states that saturate the bound if DeltaE
is not equal to E. However, the bound remains tight: for any given values of
DeltaE and E, there exists a one-parameter family of initial states that can
approach the bound arbitrarily close when the parameter approaches its limit
value. The relation between the largest energy level, the average energy, and
the orthogonalization time is also discussed. These results establish the
fundamental quantum limit on the rate of operation of any
information-processing system.Comment: 4 pages 1 PS figure Late
Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
We extend the Keldysh technique to enable the computation of out-of-time
order correlators. We show that the behavior of these correlators is described
by equations that display initially an exponential instability which is
followed by a linear propagation of the decoherence between two initially
identically copies of the quantum many body systems with interactions. At large
times the decoherence propagation (quantum butterfly effect) is described by a
diffusion equation with non-linear dissipation known in the theory of
combustion waves. The solution of this equation is a propagating non-linear
wave moving with constant velocity despite the diffusive character of the
underlying dynamics. Our general conclusions are illustrated by the detailed
computations for the specific models describing the electrons interacting with
bosonic degrees of freedom (phonons, two-level-systems etc.) or with each
other
Frustration and glassiness in spin models with cavity-mediated interactions
We show that the effective spin-spin interaction between three-level atoms
confined in a multimode optical cavity is long-ranged and sign-changing, like
the RKKY interaction; therefore, ensembles of such atoms subject to frozen-in
positional randomness can realize spin systems having disordered and frustrated
interactions. We argue that, whenever the atoms couple to sufficiently many
cavity modes, the cavity-mediated interactions give rise to a spin glass. In
addition, we show that the quantum dynamics of cavity-confined spin systems is
that of a Bose-Hubbard model with strongly disordered hopping but no on-site
disorder; this model exhibits a random-singlet glass phase, absent in
conventional optical-lattice realizations. We briefly discuss experimental
signatures of the realizable phases.Comment: 5 pages, 2 figure
Thermodynamic cost of reversible computing
Since reversible computing requires preservation of all information
throughout the entire computational process, this implies that all errors that
appear as a result of the interaction of the information-carrying system with
uncontrolled degrees of freedom must be corrected. But this can only be done at
the expense of an increase in the entropy of the environment corresponding to
the dissipation, in the form of heat, of the ``noisy'' part of the system's
energy.
This paper gives an expression of that energy in terms of the effective noise
temperature, and analyzes the relationship between the energy dissipation rate
and the rate of computation. Finally, a generalized Clausius principle based on
the concept of effective temperature is presented.Comment: 5 pages; added two paragraphs and fixed a number of typo
Space-like and time-like pion electromagnetic form factor and Fock state components within the Light-Front dynamics
The simultaneous investigation of the pion electromagnetic form factor in the
space- and time-like regions within a light-front model allows one to address
the issue of non-valence components of the pion and photon wave functions. Our
relativistic approach is based on a microscopic vector meson dominance (VMD)
model for the dressed vertex where a photon decays in a quark-antiquark pair,
and on a simple parametrization for the emission or absorption of a pion by a
quark. The results show an excellent agreement in the space like region up to
-10 , while in time-like region the model produces reasonable
results up to 10 .Comment: 74 pages, 11 figures, use revtex
Quasiparticle poisoning and Josephson current fluctuations induced by Kondo impurities
We introduce a toy model that allows us to study the physical properties of a
spin impurity coupled to the electrons in the superconducting island. We show
that when the coupling of the spin is of the order of the superconducting gap
two almost degenerate subgap states are formed. By computing the Berry phase
that is associated with the superconducting phase rotations in this model, we
prove that these subgap states are characterized by a different charge and
demonstrate that the switching between these states has the same effect as
quasiparticle poisoning (unpoisoning) of the island. We also show that an
impurity coupled to both the island and the lead generates Josepshon current
fluctuations.Comment: 5 pages, 1 figur
Stabilization and destabilization of second-order solitons against perturbations in the nonlinear Schr\"{o}dinger equation
We consider splitting and stabilization of second-order solitons (2-soliton
breathers) in a model based on the nonlinear Schr\"{o}dinger equation (NLSE),
which includes a small quintic term, and weak resonant nonlinearity management
(NLM), i.e., time-periodic modulation of the cubic coefficient, at the
frequency close to that of shape oscillations of the 2-soliton. The model
applies to the light propagation in media with cubic-quintic optical
nonlinearities and periodic alternation of linear loss and gain, and to BEC,
with the self-focusing quintic term accounting for the weak deviation of the
dynamics from one-dimensionality, while the NLM can be induced by means of the
Feshbach resonance. We propose an explanation to the effect of the resonant
splitting of the 2-soliton under the action of the NLM. Then, using systematic
simulations and an analytical approach, we conclude that the weak quintic
nonlinearity with the self-focusing sign stabilizes the 2-soliton, while the
self-defocusing quintic nonlinearity accelerates its splitting. It is also
shown that the quintic term with the self-defocusing/focusing sign makes the
resonant response of the 2-soliton to the NLM essentially broader, in terms of
the frequency.Comment: 16 pages, 6 figure
Could Only Fermions Be Elementary?
In standard Poincare and anti de Sitter SO(2,3) invariant theories,
antiparticles are related to negative energy solutions of covariant equations
while independent positive energy unitary irreducible representations (UIRs) of
the symmetry group are used for describing both a particle and its
antiparticle. Such an approach cannot be applied in de Sitter SO(1,4) invariant
theory. We argue that it would be more natural to require that (*) one UIR
should describe a particle and its antiparticle simultaneously. This would
automatically explain the existence of antiparticles and show that a particle
and its antiparticle are different states of the same object. If (*) is adopted
then among the above groups only the SO(1,4) one can be a candidate for
constructing elementary particle theory. It is shown that UIRs of the SO(1,4)
group can be interpreted in the framework of (*) and cannot be interpreted in
the standard way. By quantizing such UIRs and requiring that the energy should
be positive in the Poincare approximation, we conclude that i) elementary
particles can be only fermions. It is also shown that ii) C invariance is not
exact even in the free massive theory and iii) elementary particles cannot be
neutral. This gives a natural explanation of the fact that all observed neutral
states are bosons.Comment: The paper is considerably revised and the following results are
added: in the SO(1,4) invariant theory i) the C invariance is not exact even
for free massive particles; ii) neutral particles cannot be elementar
Backward Evolving Quantum States
The basic concept of the two-state vector formalism, which is the time
symmetric approach to quantum mechanics, is the backward evolving quantum
state. However, due to the time asymmetry of the memory's arrow of time, the
possible ways to manipulate a backward evolving quantum state differ from those
for a standard, forward evolving quantum state. The similarities and the
differences between forward and backward evolving quantum states regarding the
no-cloning theorem, nonlocal measurements, and teleportation are discussed. The
results are relevant not only in the framework of the two-state vector
formalism, but also in the framework of retrodictive quantum theory.Comment: Contribution to the J.Phys. A special issue in honor of GianCarlo
Ghirard
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