1,525 research outputs found
The classical-quantum divergence of complexity in modelling spin chains
The minimal memory required to model a given stochastic process - known as
the statistical complexity - is a widely adopted quantifier of structure in
complexity science. Here, we ask if quantum mechanics can fundamentally change
the qualitative behaviour of this measure. We study this question in the
context of the classical Ising spin chain. In this system, the statistical
complexity is known to grow monotonically with temperature. We evaluate the
spin chain's quantum mechanical statistical complexity by explicitly
constructing its provably simplest quantum model, and demonstrate that this
measure exhibits drastically different behaviour: it rises to a maximum at some
finite temperature then tends back towards zero for higher temperatures. This
demonstrates how complexity, as captured by the amount of memory required to
model a process, can exhibit radically different behaviour when quantum
processing is allowed.Comment: 9 pages, 3 figures, comments are welcom
The LeChatelier principle: The long and the short of it
Using ordinary calculus techniques, we investigate the conditions under which LeChatelier effects are signable for finite changes in parameter values. We show, for example, that the short run demand for a factor is always less responsive to price changes than the long run demand, provided that the factor of production and the fixed factor do not switch from being substitutes to being complements (or vice versa) over the relevant range of the price change. The absence of a sign change in the complementarity/substitutability relation holds under conditions that are considerably more general than supermodularity of the production function.postprin
Spontaneous Interlayer Charge Transfer near the Magnetic Quantum Limit
Experiments reveal that a confined electron system with two equally-populated
layers at zero magnetic field can spontaneously break this symmetry through an
interlayer charge transfer near the magnetic quantum limit. New fractional
quantum Hall states at unusual total filling factors such as \nu = 11/15 (= 1/3
+ 2/5) stabilize as signatures that the system deforms itself, at substantial
electrostatic energy cost, in order to gain crucial correlation energy by
"locking in" separate incompressible liquid phases at unequal fillings in the
two layers (e.g., layered 1/3 and 2/5 states in the case of \nu = 11/15).Comment: 4 pages, 4 figures (1 color) included in text. Related papers at
http://www.ee.princeton.edu/~hari/papers.htm
Magnetic-Field-Induced Hybridization of Electron Subbands in a Coupled Double Quantum Well
We employ a magnetocapacitance technique to study the spectrum of the soft
two-subband (or double-layer) electron system in a parabolic quantum well with
a narrow tunnel barrier in the centre. In this system unbalanced by gate
depletion, at temperatures T\agt 30 mK we observe two sets of quantum
oscillations: one originates from the upper electron subband in the
closer-to-the-gate part of the well and the other indicates the existence of
common gaps in the spectrum at integer fillings. For the lowest filling factors
and , both the common gap presence down to the point of one- to
two-subband transition and their non-trivial magnetic field dependences point
to magnetic-field-induced hybridization of electron subbands.Comment: Major changes, added one more figure, the latest version to be
published in JETP Let
Surveying structural complexity in quantum many-body systems
Quantum many-body systems exhibit a rich and diverse range of exotic
behaviours, owing to their underlying non-classical structure. These systems
present a deep structure beyond those that can be captured by measures of
correlation and entanglement alone. Using tools from complexity science, we
characterise such structure. We investigate the structural complexities that
can be found within the patterns that manifest from the observational data of
these systems. In particular, using two prototypical quantum many-body systems
as test cases - the one-dimensional quantum Ising and Bose-Hubbard models - we
explore how different information-theoretic measures of complexity are able to
identify different features of such patterns. This work furthers the
understanding of fully-quantum notions of structure and complexity in quantum
systems and dynamics.Comment: 9 pages, 5 figure
Quantum Hall effect in single wide quantum wells
We study the quantum Hall states in the lowest Landau level for a single wide
quantum well. Due to a separation of charges to opposite sides of the well, a
single wide well can be modelled as an effective two level system. We provide
numerical evidence of the existence of a phase transition from an
incompressible to a compressible state as the electron density is increased for
specific well width. Our numerical results show a critical electron density
which depends on well width, beyond which a transition incompressible double
layer quantum Hall state to a mono-layer compressible state occurs. We also
calculate the related phase boundary corresponding to destruction of the
collective mode energy gap. We show that the effective tunneling term and the
interlayer separation are both renormalised by the strong magnetic field. We
also exploite the local density functional techniques in the presence of strong
magnetic field at to calculate renormalized . The
numerical results shows good agreement between many-body calculations and local
density functional techniques in the presence of a strong magnetic field at
. we also discuss implications of this work on the
incompressible state observed in SWQW.Comment: 30 pages, 7 figures (figures are not included
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