A staggered fermion chain with supersymmetry on open intervals

A strongly-interacting fermion chain with supersymmetry on the lattice and open boundary conditions is analysed. The local coupling constants of the model are staggered, and the properties of the ground states as a function of the staggering parameter are examined. In particular, a connection between certain ground-state components and solutions of non-linear recursion relations associated with the Painlev\'e VI equation is conjectured. Moreover, various local occupation probabilities in the ground state have the so-called scale-free property, and allow for an exact resummation in the limit of infinite system size.Comment: 21 pages, no figures; v2: typos correcte

Sinai model in presence of dilute absorbers

We study the Sinai model for the diffusion of a particle in a one dimension random potential in presence of a small concentration $\rho$ of perfect absorbers using the asymptotically exact real space renormalization method. We compute the survival probability, the averaged diffusion front and return probability, the two particle meeting probability, the distribution of total distance traveled before absorption and the averaged Green's function of the associated Schrodinger operator. Our work confirms some recent results of Texier and Hagendorf obtained by Dyson-Schmidt methods, and extends them to other observables and in presence of a drift. In particular the power law density of states is found to hold in all cases. Irrespective of the drift, the asymptotic rescaled diffusion front of surviving particles is found to be a symmetric step distribution, uniform for $|x| < {1/2} \xi(t)$, where $\xi(t)$ is a new, survival length scale ($\xi(t)=T \ln t/\sqrt{\rho}$ in the absence of drift). Survival outside this sharp region is found to decay with a larger exponent, continuously varying with the rescaled distance $x/\xi(t)$. A simple physical picture based on a saddle point is given, and universality is discussed.Comment: 21 pages, 2 figure

Ground-state properties of a supersymmetric fermion chain

We analyze the ground state of a strongly interacting fermion chain with a supersymmetry. We conjecture a number of exact results, such as a hidden duality between weak and strong couplings. By exploiting a scale free property of the perturbative expansions, we find exact expressions for the order parameters, yielding the critical exponents. We show that the ground state of this fermion chain and another model in the same universality class, the XYZ chain along a line of couplings, are both written in terms of the same polynomials. We demonstrate this explicitly for up to N = 24 sites, and provide consistency checks for large N. These polynomials satisfy a recursion relation related to the Painlev\'e VI differential equation, and using a scale-free property of these polynomials, we derive a simple and exact formula for their limit as N goes to infinity.Comment: v2: added more information on scaling function, fixed typo

One-dimensional classical diffusion in a random force field with weakly concentrated absorbers

A one-dimensional model of classical diffusion in a random force field with a weak concentration $\rho$ of absorbers is studied. The force field is taken as a Gaussian white noise with \mean{\phi(x)}=0 and \mean{\phi(x)\phi(x')}=g \delta(x-x'). Our analysis relies on the relation between the Fokker-Planck operator and a quantum Hamiltonian in which absorption leads to breaking of supersymmetry. Using a Lifshits argument, it is shown that the average return probability is a power law \smean{P(x,t|x,0)}\sim{}t^{-\sqrt{2\rho/g}} (to be compared with the usual Lifshits exponential decay $\exp{-(\rho^2t)^{1/3}}$ in the absence of the random force field). The localisation properties of the underlying quantum Hamiltonian are discussed as well.Comment: 6 pages, LaTeX, 5 eps figure

A pilot study exploring the role of glucocorticoid receptor variants in primary biliary cirrhosis and primary sclerosing cholangitis

BACKGROUND: In primary biliary cirrhosis (PBC) and primary sclerosing cholangitis (PSC) significant therapeutic effects of glucocorticoids have not been documented. The most important clinical problem in patients with these diseases is fatigue, which is occasionally invalidating. Abnormalities in the hypothalamo-pituitary-adrenal axis have been suggested as a cause of fatigue. Most effects of glucocorticoids are mediated by the glucocorticoid receptor (hGR alpha). Recently a causative role for a splicing variant of the glucocorticoid receptor (hGR beta) has been proposed in glucocorticoid resistance in asthma and ulcerative colitis, whereas another splicing variant (hGR P) might be associated with glucocorticoid-resistant haematological malignancies. The aims of the present pilot study were to assess abnormalities in glucocorticoid receptor expression and to relate these abnormalities to the development of fatigue and to disease activity and severity in autoimmune cholestatic liver disease. METHODS: Five fatigued and five nonfatigued patients with PBC or PSC were included, and the results were compared with healthy controls. RESULTS: The expression of hGR P was not different from controls, but hGR beta mRNA was significantly increased (p=0.02) and hGR alpha mRNA decreased (p=0.015). There were no significant differences between fatigued and nonfatigued patients. A significant negative correlation between the serum activity of alkaline phosphatase and hGR alpha and hGR P mRNA was found. CONCLUSION: Although there was no relation with fatigue, abnormalities in hGR expression appear to occur in patients with these diseases, and may play a role in its pathophysiology and the poor response to glucocorticoid treatment

Fluctuation force exerted by a planar self-avoiding polymer

Using results from Schramm Loewner evolution (SLE), we give the expression of the fluctuation-induced force exerted by a polymer on a small impenetrable disk, in various 2-dimensional domain geometries. We generalize to two polymers and examine whether the fluctuation force can trap the object into a stable equilibrium. We compute the force exerted on objects at the domain boundary, and the force mediated by the polymer between such objects. The results can straightforwardly be extended to any SLE interface, including Ising, percolation, and loop-erased random walks. Some are relevant for extremal value statistics.Comment: 7 pages, 22 figure

Was ging in ihm vor? Laientheorien über kognitive und emotionale Vorgänge eines Selbstmörders

Tested Rational-Emotive Behavior Therapy’s (REBT; Ellis, 1962, 1994) assumption that irrational beliefs and maladaptive emotions are associated with dysfunctional behaviors, whereas rational cognitions and adaptive emotions lead to functional actions. Participants read newspaper articles about the defeat of a boxer. In one condition, the (authentic) article informed participants that he committed suicide, and in a second (fictitious) article about the same defeat, the athlete was described as successfully resuming his career. Participants’ assumptions about the stimulus person’s defeat-related cognitions and emotions were assessed on rating scales and via sentence completion and free responses. Participants responding to the suicide scenario assumed significantly more irrational beliefs (e.g., ”I absolutely have to win”) on the side of the boxer regarding his defeat than controls in the fictitious non-suicide version. This finding was obtained by all assessment methods. Additionally, participants expected the suicidal stimulus person to be experiencing maladaptive emotions (e.g., depression, guilt), whereas the stimulus person who successfully resumed his career was expected to experience adaptive affects (e.g., sadness, concern). Subsequent ratings of the functionality of selected emotions revealed that sadness, fear, annoyance, and concern were rated to be more functional than depression, anxiety, rage, and guilt.In einer Fragebogenstudie wurden den Teilnehmenden reale Zeitungsartikel vorgelegt, die vom Selbstmord eines besiegten Boxers berichteten. Die Probanden sollten sich in die Person des Sportlers hineinversetzen und die Gedanken und Gefühle schildern, die sie bei ihm in Zusammenhang mit der Niederlage erwarteten. Die Probanden vermuteten bei dem Sportler durchgängig in höherer Weise irrationale rigide Gedanken (z.B. „ich muss unbedingt siegen“) als rationales Denken (z.B. „ich möchte gerne siegen“) und eher maladaptive Emotionen (Angst, Wut, Depression und Schuld) als adaptive Emotionen (Furcht, Ärger, Trauer und Bedauern). Dies trat jedoch nur dann ein, wenn in den Zeitungsartikeln nachfolgendes dysfunktionales Verhalten des Boxers (Suizid) geschildert wurde: In einer Kontrollbedingung, die ebenfalls von der Niederlage – allerdings mit erfolgreicher Fortsetzung der Boxerkarriere – berichtet, zeigte sich dieses Datenmuster nicht. Diese Befunde entsprechen den theoretischen Annahmen und Vorhersagen der Rational-Emotiven-Verhaltenstherapie (REVT) von Albert Ellis. Zusätzlich erhobene Daten zur generellen Funktionalität der acht Emotionen bestätigen ebenfalls die theoretischen Annahmen

Lyapunov exponents, one-dimensional Anderson localisation and products of random matrices

The concept of Lyapunov exponent has long occupied a central place in the theory of Anderson localisation; its interest in this particular context is that it provides a reasonable measure of the localisation length. The Lyapunov exponent also features prominently in the theory of products of random matrices pioneered by Furstenberg. After a brief historical survey, we describe some recent work that exploits the close connections between these topics. We review the known solvable cases of disordered quantum mechanics involving random point scatterers and discuss a new solvable case. Finally, we point out some limitations of the Lyapunov exponent as a means of studying localisation properties.Comment: LaTeX, 23 pages, 3 pdf figures ; review for a special issue on "Lyapunov analysis" ; v2 : typo corrected in eq.(3) & minor change