Transmission and Reflection in the Stadium Billiard: Time-dependent asymmetric transport

We investigate the transmission and reflection survival probabilities for the chaotic stadium billiard with two holes placed asymmetrically. Classically, these distributions are shown to have algebraic or exponential decays depending on the choice of injecting hole and exact expressions are given for the first time and confirmed numerically. As there is no reported quantum theoretical or experimental analogue we propose a model for experimental observation of the asymmetric transport using semiconductor nano-structures and comment on the relevant quantum time-scales.Comment: 4 pages, 4 figure

Coulomb correlation in presence of spin-orbit coupling: application to plutonium

Attempts to go beyond the local density approximation (LDA) of Density Functional Theory (DFT) have been increasingly based on the incorporation of more realistic Coulomb interactions. In their earliest implementations, methods like LDA+$U$, LDA + DMFT (Dynamical Mean Field Theory), and LDA+Gutzwiller used a simple model interaction $U$. In this article we generalize the solution of the full Coulomb matrix involving $F^{(0)}$ to $F^{(6)}$ parameters, which is usually presented in terms of an $\ell m_\ell$ basis, into a $jm_{j}$ basis of the total angular momentum, where we also include spin-orbit coupling; this type of theory is needed for a reliable description of $f$-state elements like plutonium, which we use as an example of our theory. Close attention will be paid to spin-flip terms, which are important in multiplet theory but that have been usually neglected in these kinds of studies. We find that, in a density-density approximation, the $jm_j$ basis results provide a very good approximation to the full Coulomb matrix result, in contrast to the much less accurate results for the more conventional $\ell m_\ell$ basis

Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study

Motivated by experimental studies that have found signatures of a quantum spin liquid phase in organic crystals whose structure is well described by the two-dimensional triangular lattice, we study the Hubbard model on this lattice at half filling using the infinite-system density matrix renormalization group (iDMRG) method. On infinite cylinders with finite circumference, we identify an intermediate phase between observed metallic behavior at low interaction strength and Mott insulating spin-ordered behavior at strong interactions. Chiral ordering from spontaneous breaking of time-reversal symmetry, a fractionally quantized spin Hall response, and characteristic level statistics in the entanglement spectrum in the intermediate phase provide strong evidence for the existence of a chiral spin liquid in the full two-dimensional limit of the model.Comment: v2: 15 pages, 13 figures, plus 30 pages (38 figures) Supplemental Material. Substantial additional data supporting the original conclusions: additional cylinder geometries; flux insertion; MPS transfer matrix spectra; analysis of the metal-insulator transition; and analysis of domain walls between the two chiralities. v1:7 pages, 4 figures, plus 15 pages (22 figures) Supplementary Materia

Psychopolitics: Peter Sedgwick’s legacy for mental health movements

This paper re-considers the relevance of Peter Sedgwick's Psychopolitics (1982) for a politics of mental health. Psychopolitics offered an indictment of ‘anti-psychiatry’ the failure of which, Sedgwick argued, lay in its deconstruction of the category of ‘mental illness’, a gesture that resulted in a politics of nihilism. ‘The radical who is only a radical nihilist’, Sedgwick observed, ‘is for all practical purposes the most adamant of conservatives’. Sedgwick argued, rather, that the concept of ‘mental illness’ could be a truly critical concept if it was deployed ‘to make demands upon the health service facilities of the society in which we live’. The paper contextualizes Psychopolitics within the ‘crisis tendencies’ of its time, surveying the shifting welfare landscape of the subsequent 25 years alongside Sedgwick's continuing relevance. It considers the dilemma that the discourse of ‘mental illness’ – Sedgwick's critical concept – has fallen out of favour with radical mental health movements yet remains paradigmatic within psychiatry itself. Finally, the paper endorses a contemporary perspective that, while necessarily updating Psychopolitics, remains nonetheless ‘Sedgwickian’

Billiards with polynomial mixing rates

While many dynamical systems of mechanical origin, in particular billiards, are strongly chaotic -- enjoy exponential mixing, the rates of mixing in many other models are slow (algebraic, or polynomial). The dynamics in the latter are intermittent between regular and chaotic, which makes them particularly interesting in physical studies. However, mathematical methods for the analysis of systems with slow mixing rates were developed just recently and are still difficult to apply to realistic models. Here we reduce those methods to a practical scheme that allows us to obtain a nearly optimal bound on mixing rates. We demonstrate how the method works by applying it to several classes of chaotic billiards with slow mixing as well as discuss a few examples where the method, in its present form, fails.Comment: 39pages, 11 figue

Open Mushrooms: Stickiness revisited

We investigate mushroom billiards, a class of dynamical systems with sharply divided phase space. For typical values of the control parameter of the system $\rho$, an infinite number of marginally unstable periodic orbits (MUPOs) exist making the system sticky in the sense that unstable orbits approach regular regions in phase space and thus exhibit regular behaviour for long periods of time. The problem of finding these MUPOs is expressed as the well known problem of finding optimal rational approximations of a real number, subject to some system-specific constraints. By introducing a generalized mushroom and using properties of continued fractions, we describe a zero measure set of control parameter values $\rho\in(0,1)$ for which all MUPOs are destroyed and therefore the system is less sticky. The open mushroom (billiard with a hole) is then considered in order to quantify the stickiness exhibited and exact leading order expressions for the algebraic decay of the survival probability function $P(t)$ are calculated for mushrooms with triangular and rectangular stems.Comment: 21 pages, 11 figures. Includes discussion of a three-dimensional mushroo

The counterphobic defense in children

The clinical data for this study were derived from the case histories of five children who consistently used the counterphobic defense either alone or in combination with phobic attitudes. The children's manifestations of this defense appeared in both verbal and nonverbal behavioral patterns. The choice of defensive style was found related to at least three factors: an early history of trauma, especially separation, parental encouragement of “toughness,” and essentially a counterphobic family style.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43947/1/10578_2005_Article_BF01433642.pd

Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces.

yesThe orthocomplemented modular lattice of subspaces L[H(d)] , of a quantum system with d-dimensional Hilbert space H(d), is considered. A generalized additivity relation which holds for Kolmogorov probabilities is violated by quantum probabilities in the full lattice L[H(d)] (it is only valid within the Boolean subalgebras of L[H(d)] ). This suggests the use of more general (than Kolmogorov) probability theories, and here the Dempster-Shafer probability theory is adopted. An operator D(H1,H2) , which quantifies deviations from Kolmogorov probability theory is introduced, and it is shown to be intimately related to the commutator of the projectors P(H1),P(H2) , to the subspaces H 1, H 2. As an application, it is shown that the proof of the inequalities of Clauser, Horne, Shimony, and Holt for a system of two spin 1/2 particles is valid for Kolmogorov probabilities, but it is not valid for Dempster-Shafer probabilities. The violation of these inequalities in experiments supports the interpretation of quantum probabilities as Dempster-Shafer probabilities