Heun and Mathieu functions as solutions of the Dirac equation

We give examples of where the Heun function exists as solutions of wave equations encountered in general relativity. While the Dirac equation written in the background of Nutku helicoid metric yields Mathieu functions as its solutions in four spacetime dimensions, the trivial generalization to five dimensions results in the double confluent Heun function. We reduce this solution to the Mathieu function with some transformations. We must apply Atiyah-Patodi-Singer spectral boundary conditions to this system since the metric has a singularity at the origin.Comment: 5 pages, Prepared for the Spanish Relativity Meeting (ERE 2007), Tenerife, Spain, 10-14 Sep 200

Voluntary nicotine consumption triggers in vivo potentiation of cortical excitatory drives to midbrain dopaminergic neurons

International audienceActive response to either natural or pharmacological reward causes synaptic modifications to excitatory synapses on dopamine (DA) neurons of the ventral tegmental area (VTA). Here, we examine these modifications using nicotine, the main addictive component of tobacco, which is a potent regulator of VTA DA neurons. Using an in vivo electrophysiological technique, we investigated the role of key components of the limbic circuit, the infralimbic cortex (ILCx) and the bed nucleus of the stria terminalis (BNST), in operant behaviors related to nicotine reward. Our results indicated that nicotine self-administration in rats, but not passive delivery, triggers hyperactivity of VTA DA neurons. The data suggest that potentiation of the ILCx-BNST excitatory pathway is involved in these modifications in VTA DA neurons. Thus, recruitment of these specific excitatory inputs to VTA DA neurons may be a neural correlate for the learned association between active responding and the reward experience

Spin dynamics of molecular nanomagnets fully unraveled by four-dimensional inelastic neutron scattering

Molecular nanomagnets are among the first examples of spin systems of finite size and have been test-beds for addressing a range of elusive but important phenomena in quantum dynamics. In fact, for short-enough timescales the spin wavefunctions evolve coherently according to the an appropriate cluster spin-Hamiltonian, whose structure can be tailored at the synthetic level to meet specific requirements. Unfortunately, to this point it has been impossible to determine the spin dynamics directly. If the molecule is sufficiently simple, the spin motion can be indirectly assessed by an approximate model Hamiltonian fitted to experimental measurements of various types. Here we show that recently-developed instrumentation yields the four-dimensional inelastic-neutron scattering function S(Q,E) in vast portions of reciprocal space and enables the spin dynamics to be determined with no need of any model Hamiltonian. We exploit the Cr8 antiferromagnetic ring as a benchmark to demonstrate the potential of this new approach. For the first time we extract a model-free picture of the quantum dynamics of a molecular nanomagnet. This allows us, for example, to examine how a quantum fluctuation propagates along the ring and to directly test the degree of validity of the N\'{e}el-vector-tunneling description of the spin dynamics

Tunable Excitons in Biased Bilayer Graphene

Recent measurements have shown that a continuously tunable bandgap of up to 250 meV can be generated in biased bilayer graphene [Y. Zhang et al., Nature 459, 820 (2009)], opening up pathway for possible graphene-based nanoelectronic and nanophotonic devices operating at room temperature. Here, we show that the optical response of this system is dominated by bound excitons. The main feature of the optical absorbance spectrum is determined by a single symmetric peak arising from excitons, a profile that is markedly different from that of an interband transition picture. Under laboratory conditions, the binding energy of the excitons may be tuned with the external bias going from zero to several tens of meV's. These novel strong excitonic behaviors result from a peculiar, effective ``one-dimensional'' joint density of states and a continuously-tunable bandgap in biased bilayer graphene. Moreover, we show that the electronic structure (level degeneracy, optical selection rules, etc.) of the bound excitons in a biased bilayer graphene is markedly different from that of a two-dimensional hydrogen atom because of the pseudospin physics

Singularity Structure and Stability Analysis of the Dirac Equation on the Boundary of the Nutku Helicoid Solution

Dirac equation written on the boundary of the Nutku helicoid space consists of a system of ordinary differential equations. We tried to analyze this system and we found that it has a higher singularity than those of the Heun's equations which give the solutions of the Dirac equation in the bulk. We also lose an independent integral of motion on the boundary. This facts explain why we could not find the solution of the system on the boundary in terms of known functions. We make the stability analysis of the helicoid and catenoid cases and end up with an appendix which gives a new example where one encounters a form of the Heun equation.Comment: Version to appear in JM

Electron Anomalous Magnetic Moment in Basis Light-Front Quantization Approach

We apply the Basis Light-Front Quantization (BLFQ) approach to the Hamiltonian field theory of Quantum Electrodynamics (QED) in free space. We solve for the mass eigenstates corresponding to an electron interacting with a single photon in light-front gauge. Based on the resulting non-perturbative ground state light-front amplitude we evaluate the electron anomalous magnetic moment. The numerical results from extrapolating to the infinite basis limit reproduce the perturbative Schwinger result with relative deviation less than 0.6%. We report significant improvements over previous works including the development of analytic methods for evaluating the vertex matrix elements of QED.Comment: 6 pages, 1 figure, proceeding for Lightcone 2011 conferenc

Mesopontine rostromedial tegmental nucleus neurons projecting to the dorsal raphe and pedunculopontine tegmental nucleus: psychostimulant-elicited Fos expression and collateralization

The mesopontine rostromedial tegmental nucleus (RMTg) is a GABAergic structure in the ventral midbrain and rostral pons that, when activated, inhibits dopaminergic neurons in the ventral tegmental area and substantia nigra compacta. Additional strong outputs from the RMTg to the pedunculopontine tegmental nucleus pars dissipata, dorsal raphe nucleus, and the pontomedullary gigantocellular reticular formation were identified by anterograde tracing. RMTg neurons projecting to the ventral tegmental area express the immediate early gene Fos upon psychostimulant administration. The present study was undertaken to determine if neurons in the RMTg that project to the additional structures listed above also express Fos upon psychostimulant administration and, if so, whether single neurons in the RMTg project to more than one of these structures. We found that about 50% of RMTg neurons exhibiting retrograde labeling after injections of retrograde tracer in the dorsal raphe or pars dissipata of the pedunculopontine tegmental nucleus express Fos after acute methamphetamine exposure. Also, we observed that a significant number of RMTg neurons project both to the ventral tegmental area and one of these structures. In contrast, methamphetamine-elicited Fos expression was not observed in RMTg neurons labeled with retrograde tracer following injections into the pontomedullary reticular formation. The findings suggest that the RMTg is an integrative modulator of multiple rostrally projecting structures

Thermal and near-infrared light induced spin crossover in a mononuclear iron( ii ) complex with a tetrathiafulvalene-fused dipyridophenazine ligand

A mononuclear Fe(II) complex involving a tetrathiafulvalene-based ligand exhibits thermal spin-crossover (around 143 K) with pronounced hysteresis behaviour (48 K). The chromophoric and π-extended ligand allows Near-Infrared (NIR) sensitization for the light-induced excited spin-state trapping (LIESST) with T(LIESST) = 90 K

Severe stress switches CRF action in the nucleus accumbens from appetitive to aversive.

Stressors motivate an array of adaptive responses ranging from \u27fight or flight\u27 to an internal urgency signal facilitating long-term goals. However, traumatic or chronic uncontrollable stress promotes the onset of major depressive disorder, in which acute stressors lose their motivational properties and are perceived as insurmountable impediments. Consequently, stress-induced depression is a debilitating human condition characterized by an affective shift from engagement of the environment to withdrawal. An emerging neurobiological substrate of depression and associated pathology is the nucleus accumbens, a region with the capacity to mediate a diverse range of stress responses by interfacing limbic, cognitive and motor circuitry. Here we report that corticotropin-releasing factor (CRF), a neuropeptide released in response to acute stressors and other arousing environmental stimuli, acts in the nucleus accumbens of naive mice to increase dopamine release through coactivation of the receptors CRFR1 and CRFR2. Remarkably, severe-stress exposure completely abolished this effect without recovery for at least 90 days. This loss of CRF\u27s capacity to regulate dopamine release in the nucleus accumbens is accompanied by a switch in the reaction to CRF from appetitive to aversive, indicating a diametric change in the emotional response to acute stressors. Thus, the current findings offer a biological substrate for the switch in affect which is central to stress-induced depressive disorders

Expression of amphetamine sensitization is associated with recruitment of a reactive neuronal population in the nucleus accumbens core

Rationale: Repeated exposure to psychostimulant drugs causes a long-lasting increase in the psychomotor and reinforcing effects of these drugs and an array of neuroadaptations. One such alteration is a hypersensitivity of striatal activity such that a low dose of amphetamine in sensitized animals produces dorsal striatal activation patterns similar to acute treatment with a high dose of amphetamine. Objectives: To extend previous findings of striatal hypersensitivity with behavioral observations and with cellular activity in the nucleus accumbens and prefrontal cortex in sensitized animals. Materials and methods: Rats treated acutely with 0, 1, 2.5, or 5 mg/kg i.p. amphetamine and sensitized rats challenged with 1 mg/kg i.p. amphetamine were scored for stereotypy, rearing, and grooming, and locomotor activity recorded. c-fos positive nuclei were quantified in the nucleus accumbens and prefrontal cortex after expression of sensitization with 1 mg/kg i.p. amphetamine. Results: Intense stereotypy was seen in animals treated acutely with 5 mg/kg amphetamine, but not in the sensitized group treated with 1 mg/kg amphetamine. The c-fos response to amphetamine in the accumbens core was augmented in amphetamine-pretreated animals with a shift in the distribution of optical density, while no effect of sensitization was seen in the nucleus accumbens shell or prefrontal cortex. Conclusions A lack of stereotypy in the sensitized group indicates a dissociation of behavioral responses to amphetamine and striatal immediate-early gene activation patterns. The increase in c-fos positive nuclei and shift in the distribution of optical density observed in the nucleus accumbens core suggests recruitment of a new population of neurons during expression of sensitization