Uncertainty Relation for the Discrete Fourier Transform

We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=exp[i phi] VU. Its most important application is to constrain how much a quantum state can be localised simultaneously in two mutually unbiased bases related by a Discrete Fourier Transform. It provides an uncertainty relation which smoothly interpolates between the well known cases of the Pauli operators in 2 dimensions and the continuous variables position and momentum. This work also provides an uncertainty relation for modular variables, and could find applications in signal processing. In the finite dimensional case the minimum uncertainty states, discrete analogues of coherent and squeezed states, are minimum energy solutions of Harper's equation, a discrete version of the Harmonic oscillator equation.Comment: Extended Version; 13 pages; In press in Phys. Rev. Let

Effect of deuterium on the circadian period and metabolism in wild-type and tau mutant Syrian hamsters

Homozygous tau mutant Syrian hamsters (tau-/-) have a free-running circadian period (τ) around 20 h and a proportionally higher metabolic rate compared with wild-type hamsters (tau+/+) with a period of circa 24 h. In this study, we applied deuterium oxide (D2O) to hamsters to test whether deuteration affects the circadian period of locomotor activity and metabolic rate in both genotypes. Running wheel activity and the metabolic rate were measured in constant illumination before, during, and after administration of 25% deuterium in drinking water. Wild-type hamsters lengthened their circadian period by 1.19 h (SD = 0.29 h) due to D2O application and tau-/- hamsters by 1.20 h (SD = 0.39 h). Deuteration changed neither the amount of activity nor the duration of activity phase (α) in either genotype. The mass specific average metabolic rate (AMR, the oxygen consumption over 24 h) and the mass specific resting metabolic rate (RMR) did not differ during deuteration compared with non-deuteration conditions for either genotype. Both with and without D2O, tau-/- hamsters had higher metabolic rates than tau+/+ hamsters. There was no correlation between changes in the circadian period of locomotor activity and metabolic rates caused by D2O.

Cocaine Addiction as a Homeostatic Reinforcement Learning Disorder

Drug addiction implicates both reward learning and homeostatic regulation mechanisms of the brain. This has stimulated 2 partially successful theoretical perspectives on addiction. Many important aspects of addiction, however, remain to be explained within a single, unified framework that integrates the 2 mechanisms. Building upon a recently developed homeostatic reinforcement learning theory, the authors focus on a key transition stage of addiction that is well modeled in animals, escalation of drug use, and propose a computational theory of cocaine addiction where cocaine reinforces behavior due to its rapid homeostatic corrective effect, whereas its chronic use induces slow and long-lasting changes in homeostatic setpoint. Simulations show that our new theory accounts for key behavioral and neurobiological features of addiction, most notably, escalation of cocaine use, drug-primed craving and relapse, individual differences underlying dose-response curves, and dopamine D2-receptor downregulation in addicts. The theory also generates unique predictions about cocaine self-administration behavior in rats that are confirmed by new experimental results. Viewing addiction as a homeostatic reinforcement learning disorder coherently explains many behavioral and neurobiological aspects of the transition to cocaine addiction, and suggests a new perspective toward understanding addiction

Kinetic Analysis of the Thermal Degradation of Polystyrene-Montmorillonite Nanocomposite

Nanocomposites exhibit a combination of unique properties, such as increased heat distortion temperature, reduced permeability, reduced flammability and improved mechanical properties. In this work, a polystyrene (PS) clay nanocomposite was prepared via bulk polymerization using a novel organically modified montmorillonite (MMT). The organic-modifier is the N,N-dimethyl-n-hexadecyl-(4-vinylbenzyl) ammonium chloride (VB16). The thermal stability of PS–VB16 compared to pure PS is examined in pyrolytic and thermo-oxidative conditions. It is then studied using a kinetic analysis. It is shown that the stability of PS is significantly increased in the presence of clay. The thermal behavior of PS and PS nanocomposite is modeled and simulated. A very good agreement between experimental and simulated curves both in dynamic and isothermal conditions is observed. Using kinetic analysis associated to the reaction to fire of PS nanocomposite simulated in a cone calorimeter, the peak of heat release rate is half that of virgin PS, it is suggested that the clay acts as a char promoter slowing down the degradation and providing a protective barrier to the nanocomposite. The combination of these two effects is an important factor lowering the HRR

Electron quantum dynamics in closed and open potentials at high magnetic fields: Quantization and lifetime effects unified by semicoherent states

We have developed a Green's function formalism based on the use of an overcomplete semicoherent basis of vortex states, specially devoted to the study of the Hamiltonian quantum dynamics of electrons at high magnetic fields and in an arbitrary potential landscape smooth on the scale of the magnetic length. This formalism is used here to derive the exact Green's function for an arbitrary quadratic potential in the special limit where Landau level mixing becomes negligible. This solution remarkably embraces under a unified form the cases of confining and unconfining quadratic potentials. This property results from the fact that the overcomplete vortex representation provides a more general type of spectral decomposition of the Hamiltonian operator than usually considered. Whereas confining potentials are naturally characterized by quantization effects, lifetime effects emerge instead in the case of saddle-point potentials. Our derivation proves that the appearance of lifetimes has for origin the instability of the dynamics due to quantum tunneling at saddle points of the potential landscape. In fact, the overcompleteness of the vortex representation reveals an intrinsic microscopic irreversibility of the states synonymous with a spontaneous breaking of the time symmetry exhibited by the Hamiltonian dynamics.Comment: 19 pages, 4 figures ; a few typos corrected + some passages in Sec. V rewritte