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 $\nu=1$ and $\nu=2$, 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 $\nu=1$ to calculate renormalized $\Delta_{SAS}$. The numerical results shows good agreement between many-body calculations and local density functional techniques in the presence of a strong magnetic field at $\nu=1$. we also discuss implications of this work on the $\nu=1/2$ incompressible state observed in SWQW.Comment: 30 pages, 7 figures (figures are not included