Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator

There is recently a surge of interest to cut down the time it takes to change the state of a quantum system adiabatically. We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes designed to reproduce the initial populations at some predetermined final frequency and time, providing lower bounds and examples. Implications for the limits imposed to the process times and for the principle of unattainability of the absolute zero, in a single expansion or in quantum refrigerator cycles, are drawn.Comment: 7 pages, 6 figure

The Quantum Refrigerator: The quest for absolute zero

The scaling of the optimal cooling power of a reciprocating quantum refrigerator is sought as a function of the cold bath temperature as $T_c \to 0$. The working medium consists of noninteracting particles in a harmonic potential. Two closed-form solutions of the refrigeration cycle are analyzed, and compared to a numerical optimization scheme, focusing on cooling toward zero temperature. The optimal cycle is characterized by linear relations between the heat extracted from the cold bath, the energy level spacing of the working medium and the temperature. The scaling of the optimal cooling rate is found to be proportional to $T_c^{3/2}$ giving a dynamical interpretation to the third law of thermodynamics

Low temperature Thermodynamics in the Context of Dissipative Diamagnetism

We revisit here the effect of quantum dissipation on the much - studied problem of Landau diamagnetism, and analyze the results in the light of the third law of thermodynamics. The case of an additional parabolic potential is separately assessed. We find that dissipation arising from strong coupling of the system to its environment qualitatively alters the low-temperature thermodynamic attributes such as the entropy and the specific heat

Laboratory tests on dark energy

The physical nature of the currently observed dark energy in the universe is completely unclear, and many different theoretical models co-exist. Nevertheless, if dark energy is produced by vacuum fluctuations then there is a chance to probe some of its properties by simple laboratory tests based on Josephson junctions. These electronic devices can be used to perform `vacuum fluctuation spectroscopy', by directly measuring a noise spectrum induced by vacuum fluctuations. One would expect to see a cutoff near 1.7 THz in the measured power spectrum, provided the new physics underlying dark energy couples to electric charge. The effect exploited by the Josephson junction is a subtile nonlinear mixing effect and has nothing to do with the Casimir effect or other effects based on van der Waals forces. A Josephson experiment of the suggested type will now be built, and we should know the result within the next 3 years.Comment: 7 pages, 1 figure. Invited talk given at the 21 COE symposium 'Astrophysics as Interdisciplinary Science', Waseda University, Tokyo, 1-3 September 2005. To appear in Journal of Physics: Conference Series. Misprints in eq. (3) and (4) correcte

Electronic thermal transport in strongly correlated multilayered nanostructures

The formalism for a linear-response many-body treatment of the electronic contributions to thermal transport is developed for multilayered nanostructures. By properly determining the local heat-current operator, it is possible to show that the Jonson-Mahan theorem for the bulk can be extended to inhomogeneous problems, so the various thermal-transport coefficient integrands are related by powers of frequency (including all effects of vertex corrections when appropriate). We illustrate how to use this formalism by showing how it applies to measurements of the Peltier effect, the Seebeck effect, and the thermal conductance.Comment: 17 pages, 4 figures, submitted to Phys. Rev.

Notes on the Third Law of Thermodynamics.I

We analyze some aspects of the third law of thermodynamics. We first review both the entropic version (N) and the unattainability version (U) and the relation occurring between them. Then, we heuristically interpret (N) as a continuity boundary condition for thermodynamics at the boundary T=0 of the thermodynamic domain. On a rigorous mathematical footing, we discuss the third law both in Carath\'eodory's approach and in Gibbs' one. Carath\'eodory's approach is fundamental in order to understand the nature of the surface T=0. In fact, in this approach, under suitable mathematical conditions, T=0 appears as a leaf of the foliation of the thermodynamic manifold associated with the non-singular integrable Pfaffian form $\delta Q_{rev}$. Being a leaf, it cannot intersect any other leaf $S=$ const. of the foliation. We show that (N) is equivalent to the requirement that T=0 is a leaf. In Gibbs' approach, the peculiar nature of T=0 appears to be less evident because the existence of the entropy is a postulate; nevertheless, it is still possible to conclude that the lowest value of the entropy has to belong to the boundary of the convex set where the function is defined.Comment: 29 pages, 2 figures; RevTex fil

Diffuse-Charge Dynamics in Electrochemical Systems

The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate, blocking electrodes which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The ``weakly nonlinear'' limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter $\epsilon = \lambda_D/L$, where $\lambda_D$ is the screening length and $L$ the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of $\lambda_D L / D$ (not $\lambda_D^2/D$), where $D$ is the ionic diffusivity, but nonlinearity violates this common picture and introduce multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, $L^2/D$. In the ``strongly nonlinear'' regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multi-component electrolytes, and Faradaic processes.Comment: 10 figs, 26 pages (double-column), 141 reference

Cosmological Dark Energy: Prospects for a Dynamical Theory

We present an approach to the problem of vacuum energy in cosmology, based on dynamical screening of Lambda on the horizon scale. We review first the physical basis of vacuum energy as a phenomenon connected with macroscopic boundary conditions, and the origin of the idea of its screening by particle creation and vacuum polarization effects. We discuss next the relevance of the quantum trace anomaly to this issue. The trace anomaly implies additional terms in the low energy effective theory of gravity, which amounts to a non-trivial modification of the classical Einstein theory, fully consistent with the Equivalence Principle. We show that the new dynamical degrees of freedom the anomaly contains provide a natural mechanism for relaxing Lambda to zero on cosmological scales. We consider possible signatures of the restoration of conformal invariance predicted by the fluctuations of these new scalar degrees of freedom on the spectrum and statistics of the CMB, in light of the latest bounds from WMAP. Finally we assess the prospects for a new cosmological model in which the dark energy adjusts itself dynamically to the cosmological horizon boundary, and therefore remains naturally of order H^2 at all times without fine tuning.Comment: 50 pages, Invited Contribution to New Journal of Physics Focus Issue on Dark Energ

Movement and Fluctuations of the Vacuum

Quantum fields possess zero-point or vacuum fluctuations which induce mechanical effects, namely generalised Casimir forces, on any scatterer. Symmetries of vacuum therefore raise fundamental questions when confronted with the principle of relativity of motion in vacuum. The specific case of uniformly accelerated motion is particularly interesting, in connection with the much debated question of the appearance of vacuum in accelerated frames. The choice of Rindler representation, commonly used in General Relativity, transforms vacuum fluctuations into thermal fluctuations, raising difficulties of interpretation. In contrast, the conformal representation of uniformly accelerated frames fits the symmetry properties of field propagation and quantum vacuum and thus leads to extend the principle of relativity of motion to uniform accelerations. Mirrors moving in vacuum with a non uniform acceleration are known to radiate. The associated radiation reaction force is directly connected to fluctuating forces felt by motionless mirrors through fluctuation-dissipation relations. Scatterers in vacuum undergo a quantum Brownian motion which describes irreducible quantum fluctuations. Vacuum fluctuations impose ultimate limitations on measurements of position in space-time, and thus challenge the very concept of space-time localisation within a quantum framework. For test masses greater than Planck mass, the ultimate limit in localisation is determined by gravitational vacuum fluctuations. Not only positions in space-time, but also geodesic distances, behave as quantum variables, reflecting the necessary quantum nature of an underlying geometry.Comment: 17 pages, to appear in Reports on Progress in Physic

Clinical Relevance of Dissolution Testing in Quality by Design

Quality by design (QbD) has recently been introduced in pharmaceutical product development in a regulatory context and the process of implementing such concepts in the drug approval process is presently on-going. This has the potential to allow for a more flexible regulatory approach based on understanding and optimisation of how design of a product and its manufacturing process may affect product quality. Thus, adding restrictions to manufacturing beyond what can be motivated by clinical quality brings no benefits but only additional costs. This leads to a challenge for biopharmaceutical scientists to link clinical product performance to critical manufacturing attributes. In vitro dissolution testing is clearly a key tool for this purpose and the present bioequivalence guidelines and biopharmaceutical classification system (BCS) provides a platform for regulatory applications of in vitro dissolution as a marker for consistency in clinical outcomes. However, the application of these concepts might need to be further developed in the context of QbD to take advantage of the higher level of understanding that is implied and displayed in regulatory documentation utilising QbD concepts. Aspects that should be considered include identification of rate limiting steps in the absorption process that can be linked to pharmacokinetic variables and used for prediction of bioavailability variables, in vivo relevance of in vitro dissolution test conditions and performance/interpretation of specific bioavailability studies on critical formulation/process variables. This article will give some examples and suggestions how clinical relevance of dissolution testing can be achieved in the context of QbD derived from a specific case study for a BCS II compound