22,121 research outputs found
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
Mirages, anti-mirages, and further surprises in quantum corrals with non-magnetic impurities
We investigate the local density of states (LDOS) for non-interacting
electrons in a hard wall ellipse in the presence of a single non-magnetic
scattering center. Using a T-matrix analysis we calculate the local Green's
function and observe a variety of quantum mirage effects for different impurity
positions. Locating the impurity near positions with LDOS maxima for the
impurity free corral can either lead to a reduction or an enhancement of the
LDOS at the mirror image point, i.e. a mirage or anti-mirage effect, or even
suppress LDOS maxima in the entire area of the corral.Comment: 6 pages, 7 figure
Quantum Horn's lemma, finite heat baths, and the third law of thermodynamics
Interactions of quantum systems with their environment play a crucial role in
resource-theoretic approaches to thermodynamics in the microscopic regime.
Here, we analyze the possible state transitions in the presence of "small" heat
baths of bounded dimension and energy. We show that for operations on quantum
systems with fully degenerate Hamiltonian (noisy operations), all possible
state transitions can be realized exactly with a bath that is of the same size
as the system or smaller, which proves a quantum version of Horn's lemma as
conjectured by Bengtsson and Zyczkowski. On the other hand, if the system's
Hamiltonian is not fully degenerate (thermal operations), we show that some
possible transitions can only be performed with a heat bath that is unbounded
in size and energy, which is an instance of the third law of thermodynamics. In
both cases, we prove that quantum operations yield an advantage over classical
ones for any given finite heat bath, by allowing a larger and more physically
realistic set of state transitions.Comment: 15+4 pages, 6 figures. Version accepted for publication in Quantu
Higher-order interference and single-system postulates characterizing quantum theory
We present a new characterization of quantum theory in terms of simple
physical principles that is different from previous ones in two important
respects: first, it only refers to properties of single systems without any
assumptions on the composition of many systems; and second, it is closer to
experiment by having absence of higher-order interference as a postulate, which
is currently the subject of experimental investigation. We give three
postulates -- no higher-order interference, classical decomposability of
states, and strong symmetry -- and prove that the only non-classical
operational probabilistic theories satisfying them are real, complex, and
quaternionic quantum theory, together with 3-level octonionic quantum theory
and ball state spaces of arbitrary dimension. Then we show that adding
observability of energy as a fourth postulate yields complex quantum theory as
the unique solution, relating the emergence of the complex numbers to the
possibility of Hamiltonian dynamics. We also show that there may be interesting
non-quantum theories satisfying only the first two of our postulates, which
would allow for higher-order interference in experiments while still respecting
the contextuality analogue of the local orthogonality principle.Comment: 21 + 6 pages, 1 figure. v4: published version (includes several minor
corrections
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