Carnot Cycles in a Harmonically Confined Ultracold Gas across Bose-Einstein Condensation.

Carnot cycles of samples of harmonically confined ultracold 87Rb fluids, near and across Bose-Einstein condensation (BEC), are analyzed. This is achieved through the experimental determination of the corresponding equation of state in terms of the appropriate global thermodynamics for non-uniform confined fluids. We focus our attention on the efficiency of the Carnot engine when the cycle occurs for temperatures either above or below the critical temperature and when BEC is crossed during the cycle. The measurement of the cycle efficiency reveals a perfect agreement with the theoretical prediction (1-TL/TH), with TH and TL serving as the temperatures of the hot and cold heat exchange reservoirs. Other cycles are also considered for comparison.

Thermodynamic Derivation of Scaling at the Liquid-Vapor Critical Point.

With the use of thermodynamics and general equilibrium conditions only, we study the entropy of a fluid in the vicinity of the critical point of the liquid-vapor phase transition. By assuming a general form for the coexistence curve in the vicinity of the critical point, we show that the functional dependence of the entropy as a function of energy and particle densities necessarily obeys the scaling form hypothesized by Widom. Our analysis allows for a discussion of the properties of the corresponding scaling function, with the interesting prediction that the critical isotherm has the same functional dependence, between the energy and the number of particles densities, as the coexistence curve. In addition to the derivation of the expected equalities of the critical exponents, the conditions that lead to scaling also imply that, while the specific heat at constant volume can diverge at the critical point, the isothermal compressibility must do so.

Derivation of the Critical Point Scaling Hypothesis Using Thermodynamics Only.

Based on the foundations of thermodynamics and the equilibrium conditions for the coexistence of two phases in a magnetic Ising-like system, we show, first, that there is a critical point where the isothermal susceptibility diverges and the specific heat may remain finite, and second, that near the critical point the entropy of the system, and therefore all free energies, do obey scaling. Although we limit ourselves to such a system, we elaborate about the possibilities of finding universality, as well as the precise values of the critical exponents using thermodynamics only.

Nonexistence of equilibrium states at absolute negative temperatures.

We show that states of macroscopic systems with purported absolute negative temperatures are not stable under small, yet arbitrary, perturbations. We prove the previous statement using the fact that, in equilibrium, the entropy takes its maximum value. We discuss that, while Ramsey theoretical reformulation of the second law for systems with negative temperatures is logically correct, it must be a priori assumed that those states are in thermodynamic equilibrium. Since we argue that those states cannot occur, reversible processes are impossible, and, thus, Ramsey identification of absolute negative temperatures is untenable.

Robustness of multidimensional Brownian ratchets as directed transport mechanisms.

Brownian ratchets have recently been considered as models to describe the ability of certain systems to locate very specific states in multidimensional configuration spaces. This directional process has particularly been proposed as an alternative explanation for the protein folding problem, in which the polypeptide is driven toward the native state by a multidimensional Brownian ratchet. Recognizing the relevance of robustness in biological systems, in this work we analyze such a property of Brownian ratchets by pushing to the limits all the properties considered essential to produce directed transport. Based on the results presented here, we can state that Brownian ratchets are able to deliver current and locate funnel structures under a wide range of conditions. As a result, they represent a simple model that solves the Levinthal's paradox with great robustness and flexibility and without requiring any ad hoc biased transition probability. The behavior of Brownian ratchets shown in this article considerably enhances the plausibility of the model for at least part of the structural mechanism behind protein folding process.

Directed transport as a mechanism for protein folding in vivo.

We propose a model for protein folding in vivo based on a Brownian ratchet mechanism in the multidimensional energy landscape space. The device is able to produce directed transport taking advantage of the assumed intrinsic asymmetric properties of the proteins and employing the consumption of energy provided by an external source. Through such a directed transport phenomenon, the polypeptide finds the native state starting from any initial state in the energy landscape with great efficacy and robustness, even in the presence of different types of obstacles. This model solves Levinthal's paradox without requiring biased transition probabilities but at the expense of opening the system to an external field.

Thermodynamics of trapped gases: generalized mechanical variables, equation of state, and heat capacity.

We present the full thermodynamics of an interacting fluid confined by an arbitrary external potential. We show that for each confining potential, there emerge "generalized" volume and pressure variables V and P , that replace the usual volume and hydrostatic pressure of a uniform system. This scheme is validated with the derivation of the virial expansion of the grand potential. We discuss how this approach yields experimentally amenable procedures to find the equation of state of the fluid, P=P(VN,T) with N the number of atoms, as well as its heat capacity at constant generalized volume C_{V}=C_{V}(V,N,T) . With these two functions, all the thermodynamics properties of the system may be found. As specific examples we study weakly interacting Bose gases trapped by harmonic and by linear quadrupolar potentials within the Hartree-Fock approximation. We claim that this route provides an additional and useful tool to analyze both the thermodynamic variables of an ultracold trapped gas as well as its elementary excitations.

Interfacial properties of liquid-vapor interfaces with planar, spherical, and cylindrical geometries in mean field.

Following the route of the stress tensor we study the free energy of a fluid liquid-vapor interface in the van der Waals approximation for planar, cylindrical and spherical interfaces. By performing a systematic expansion in powers of the inverse of the curvature radii, and appropriately defining the Gibbs dividing surface, we find unambiguous expressions for the surface tension, the spontaneous curvature, the bending rigidity and the Gaussian rigidity.

Equation of state of an interacting bose gas confined by a harmonic trap: the role of the "harmonic" pressure.

A gas of interacting atoms confined by a three dimensional anisotropic harmonic potential is studied. It is shown that there appear "new" thermodynamic variables instead of the usual pressure and volume: the latter is replaced by (the inverse of) the cube of the geometric average of the oscillator frequencies of the trap, and the former by the harmonic pressure responsible for the mechanical equilibrium of the fluid in the trap. We discuss the origin and physical meaning of these quantities and show that the equation of state of the gas is given in terms of these variables. The equation of state of a cold gas of interacting Bose atoms in the Hartree-Fock approximation is presented. We indicate how the harmonic pressure can be measured in current experiments.

Molecular wave packet interferometry and quantum entanglement.

We study wave packet interferometry (WPI) considering the laser pulse fields both classical and quantum mechanically. WPI occurs in a molecule after subjecting it to the interaction with a sequence of phase-locked ultrashort laser pulses. Typically, the measured quantity is the fluorescence of the molecule from an excited electronic state. This signal has imprinted the interference of the vibrational wave packets prepared by the different laser pulses of the sequence. The consideration of the pulses as quantum entities in the analysis allows us to study the entanglement of the laser pulse states with the molecular states. With a simple model for the molecular system, plus several justified approximations, we solve for the fully quantum mechanical molecule-electromagnetic field state. We then study the reduced density matrices of the molecule and the laser pulses separately. We calculate measurable corrections to the case where the fields are treated classically.

Thermodynamics and phase transitions in a fluid confined by a harmonic trap.

We study a fluid of interacting atoms confined by a three-dimensional anisotropic harmonic potential, similar to those produced by the magnetic traps used to confine cold atoms. We show that instead of the usual thermodynamic variables pressure and volume, no longer existing in this case, there appear "new" variables: the volume is replaced by (the inverse cube of) the geometric average of the oscillator frequencies of the trap, and the hydrostatic pressure is replaced by an intensive variable, conjugate to the previous one, and responsible for the mechanical equilibrium of the fluid in the trap. We discuss the origin and physical meaning of these new variables. With the aid of molecular dynamics simulations we show the emergence of novel liquid, vapor and solid-like phases in a classical fluid. In particular, we calculate the liquid-vapor-like coexistence curve and show evidence for the appearance of a critical point. These phase transitions should be observable in fluids of not-so-cold alkaline atoms.

Preparation and resolution of molecular states by coherent sequences of phase-locked ultrashort laser pulses.

We study the application of nonlinear wave packet interferometry to the preparation and resolution of the overlaps of nonstationary nuclear wave functions evolving in an excited electronic state of a diatomic molecule. It is shown that possible experiments with two phase-locked ultrashort pulsepairs can be used to determine a specific vibrational wave packet state in terms of coherent states of the ground electronic state. We apply this scheme to an idealized molecule with harmonic potential energy surfaces and to the X <-- B transition states of the iodine molecule. Our results indicate that this scheme is very promising as a potential tool to quantum control.