3,169 research outputs found
Magnetoresistance and localization in bosonic insulators
We study the strong localization of hard core bosons. Using a locator
expansion we find that in the insulator, unlike for typical fermion problems,
nearly all low-energy scattering paths come with positive amplitudes and hence
interfere constructively. As a consequence, the localization length of bosonic
excitations shrinks when the constructive interference is suppressed by a
magnetic field, entailing an exponentially large positive magnetoresistance,
opposite to and significantly stronger than the analogous effect in fermions.
Within the forward scattering approximation, we find that the lowest energy
excitations are the most delocalized. A similar analysis applied to random
field Ising models suggests that the ordering transition is due to a
delocalization initiated at zero energy rather than due to the closure of a
mobility gap in the paramagnet
Stationary Algorithmic Probability
Kolmogorov complexity and algorithmic probability are defined only up to an
additive resp. multiplicative constant, since their actual values depend on the
choice of the universal reference computer. In this paper, we analyze a natural
approach to eliminate this machine-dependence.
Our method is to assign algorithmic probabilities to the different computers
themselves, based on the idea that "unnatural" computers should be hard to
emulate. Therefore, we study the Markov process of universal computers randomly
emulating each other. The corresponding stationary distribution, if it existed,
would give a natural and machine-independent probability measure on the
computers, and also on the binary strings.
Unfortunately, we show that no stationary distribution exists on the set of
all computers; thus, this method cannot eliminate machine-dependence. Moreover,
we show that the reason for failure has a clear and interesting physical
interpretation, suggesting that every other conceivable attempt to get rid of
those additive constants must fail in principle, too.
However, we show that restricting to some subclass of computers might help to
get rid of some amount of machine-dependence in some situations, and the
resulting stationary computer and string probabilities have beautiful
properties.Comment: 13 pages, 5 figures. Added an example of a positive recurrent
computer se
On the Quantum Kolmogorov Complexity of Classical Strings
We show that classical and quantum Kolmogorov complexity of binary strings
agree up to an additive constant. Both complexities are defined as the minimal
length of any (classical resp. quantum) computer program that outputs the
corresponding string.
It follows that quantum complexity is an extension of classical complexity to
the domain of quantum states. This is true even if we allow a small
probabilistic error in the quantum computer's output. We outline a mathematical
proof of this statement, based on an inequality for outputs of quantum
operations and a classical program for the simulation of a universal quantum
computer.Comment: 10 pages, no figures. Published versio
Strongly Universal Quantum Turing Machines and Invariance of Kolmogorov Complexity
We show that there exists a universal quantum Turing machine (UQTM) that can
simulate every other QTM until the other QTM has halted and then halt itself
with probability one. This extends work by Bernstein and Vazirani who have
shown that there is a UQTM that can simulate every other QTM for an arbitrary,
but preassigned number of time steps. As a corollary to this result, we give a
rigorous proof that quantum Kolmogorov complexity as defined by Berthiaume et
al. is invariant, i.e. depends on the choice of the UQTM only up to an additive
constant. Our proof is based on a new mathematical framework for QTMs,
including a thorough analysis of their halting behaviour. We introduce the
notion of mutually orthogonal halting spaces and show that the information
encoded in an input qubit string can always be effectively decomposed into a
classical and a quantum part.Comment: 18 pages, 1 figure. The operation R is now really a quantum operation
(it was not before); corrected some typos, III.B more readable, Conjecture
3.15 is now a theore
Correlating thermal machines and the second law at the nanoscale
Thermodynamics at the nanoscale is known to differ significantly from its
familiar macroscopic counterpart: the possibility of state transitions is not
determined by free energy alone, but by an infinite family of free-energy-like
quantities; strong fluctuations (possibly of quantum origin) allow to extract
less work reliably than what is expected from computing the free energy
difference. However, these known results rely crucially on the assumption that
the thermal machine is not only exactly preserved in every cycle, but also kept
uncorrelated from the quantum systems on which it acts. Here we lift this
restriction: we allow the machine to become correlated with the microscopic
systems on which it acts, while still exactly preserving its own state.
Surprisingly, we show that this restores the second law in its original form:
free energy alone determines the possible state transitions, and the
corresponding amount of work can be invested or extracted from single systems
exactly and without any fluctuations. At the same time, the work reservoir
remains uncorrelated from all other systems and parts of the machine. Thus,
microscopic machines can increase their efficiency via clever "correlation
engineering" in a perfectly cyclic manner, which is achieved by a catalytic
system that can sometimes be as small as a single qubit (though some setups
require very large catalysts). Our results also solve some open mathematical
problems on majorization which may lead to further applications in entanglement
theory.Comment: 11+13 pages, 5 figures. Added some clarifications and corrections;
results unchanged. Close to published versio
History dependence, memory and metastability in electron glasses
We discuss the history dependence and memory effects which are observed in
the out-of-equilibrium conductivity of electron glasses. The experiments can be
understood by assuming that the local density of states retains a memory of the
sample history. We provide analytical arguments for the consistency of this
assumption, and discuss the saturation of the memory effect with increasing
gate voltage change. This picture is bolstered by numerical simulations at zero
temperature, which moreover demonstrate the incompressibility of the Coulomb
glass on short timescales.Comment: 4 pages, 1 figur
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