Viscosity bound for anisotropic superfluids in higher derivative gravity

In the present paper, based on the principles of gauge/gravity duality we analytically compute the shear viscosity to entropy (eta/s) ratio corresponding to the super fluid phase in Einstein Gauss-Bonnet gravity. From our analysis we note that the ratio indeed receives a finite temperature correction below certain critical temperature (T < T-c). This proves the non universality of eta/s ratio in higher derivative theories of gravity. We also compute the upper bound for the Gauss-Bonnet coupling (lambda) corresponding to the symmetry broken phase and note that the upper bound on the coupling does not seem to change as long as we are close to the critical point of the phase diagram. However the corresponding lower bound of the eta/s ratio seems to get modified due to the finite temperature effects.

Phase diagram of the half-filled ionic Hubbard model

We study the phase diagram of the ionic Hubbard model (IHM) at half filling on a Bethe lattice of infinite connectivity using dynamical mean-field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential Delta and the on-site Hubbard U. We find that for a finite Delta and at zero temperature, long-range antiferromagnetic (AFM) order sets in beyond a threshold U = U-AF via a first-order phase transition. For U smaller than U-AF the system is a correlated band insulator. Both methods show a clear evidence for a quantum transition to a half-metal (HM) phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U. We show that the results obtained within both methods have good qualitative and quantitative consistency in the intermediate-to-strong-coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first-order phase transition at a transition temperature T-AF(U,Delta) or, equivalently, on decreasing U below U-AF(T,Delta)], within both methods, for weak to intermediate values of U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T, DMFT + CTQMC shows a second phase transition (not seen within DMFT + IPT) on increasing U beyond U-AF. At U-N > U-AF, when the Neel temperature T-N for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second-order transition. For U >> Delta, T-N similar to t(2)/U(1 - x(2)), where x = 2 Delta/U and thus T-N increases with increase in Delta/U. In the three-dimensional parameter space of (U/t, T/t, and Delta/t), as T increases, the surface of first-order transition at U-AF(T,Delta) and that of the second-order transition at U-N(T,Delta) approach each other, shrinking the range over which the AFM order is stable. There is a line of tricritical points that separates the surfaces of first- and second-order phase transitions.

Conformal perturbation theory and higher spin entanglement entropy on the torus

We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphic, conserved currents at finite temperature and on a spatial circle. For a spin-three chemical potential mu, the deformation is related at high temperatures to a higher spin black hole in hs0] theory on AdS(3) spacetime. We calculate the order mu(2) corrections to the single interval Renyi and entanglement entropies on the torus using the bosonized formulation. A consistent result, satisfying all checks, emerges upon carefully accounting for both perturbative and winding mode contributions in the bosonized language. The order mu(2) corrections involve integrals that are finite but potentially sensitive to contact term singularities. We propose and apply a prescription for defining such integrals which matches the Hamiltonian picture and passes several non-trivial checks for both thermal corrections and the Renyi entropies at this order. The thermal corrections are given by a weight six quasi-modular form, whilst the Renyi entropies are controlled by quasi-elliptic functions of the interval length with modular weight six. We also point out the well known connection between the perturbative expansion of the partition function in powers of the spin-three chemical potential and the Gross-Taylor genus expansion of large-N Yang-Mills theory on the torus. We note the absence of winding mode contributions in this connection, which suggests qualitatively different entanglement entropies for the two systems.

Isotopic fractionation in proteins as a measure of hydrogen bond length

If a deuterated molecule containing strong intramolecular hydrogen bonds is placed in a hydrogenated solvent, it may preferentially exchange deuterium for hydrogen. This preference is due to the difference between the vibrational zero-point energy for hydrogen and deuterium. It is found that the associated fractionation factor (I) is correlated with the strength of the intramolecular hydrogen bonds. This correlation has been used to determine the length of the H-bonds (donor-acceptor separation) in a diverse range of enzymes and has been argued to support the existence of short low-barrier H-bonds. Starting with a potential energy surface based on a simple diabatic state model for H-bonds, we calculate (I) as a function of the proton donor-acceptor distance R. For numerical results, we use a parameterization of the model for symmetric 0-H. ``.0 bonds R. H. McKenzie, Chem. Phys. Lett. 535, 196 (2012)]. We consider the relative contributions of the 0-H stretch vibration, O-H bend vibrations (both in plane and out of plane), tunneling splitting effects at finite temperature, and the secondary geometric isotope effect. We compare our total (I) as a function of R with NMR experimental results for enzymes, and in particular with an earlier model parametrization (D(R), used previously to determine bond lengths. (C) 2015 AIP Publishing LLC.

Fluctuation theory of Rashba Fermi gases: Gaussian and beyond

Fermi gases with generalized Rashba spin-orbit coupling induced by a synthetic gauge field have the potential of realizing many interesting states, such as rashbon condensates and topological phases. Here, we address the key open problem of the fluctuation theory of such systems and demonstrate that beyond-Gaussian effects are essential to capture the finite temperature physics of such systems. We obtain their phase diagram by constructing an approximate non-Gaussian theory. We conclusively establish that spin-orbit coupling can enhance the exponentially small transition temperature (T-c) of a weakly attracting superfluid to the order of the Fermi temperature, paving a pathway towards high T-c superfluids.

Anomalous transport at weak coupling

We evaluate the contribution of chiral fermions in d = 2, 4, 6, chiral bosons, a chiral gravitino like theory in d = 2 and chiral gravitinos in d = 6 to all the leading parity odd transport coefficients at one loop. This is done by using finite temperature field theory to evaluate the relevant Kubo formulae. For chiral fermions and chiral bosons the relation between the parity odd transport coefficient and the microscopic anomalies including gravitational anomalies agree with that found by using the general methods of hydrodynamics and the argument involving the consistency of the Euclidean vacuum. For the gravitino like theory in d = 2 and chiral gravitinos in d = 6, we show that relation between the pure gravitational anomaly and parity odd transport breaks down. From the perturbative calculation we clearly identify the terms that contribute to the anomaly polynomial, but not to the transport coefficient for gravitinos. We also develop a simple method for evaluating the angular integrals in the one loop diagrams involved in the Kubo formulae. Finally we show that charge diffusion mode of an ideal 2 dimensional Weyl gas in the presence of a finite chemical potential acquires a speed, which is equal to half the speed of light.

Lattice quantum codes and exotic topological phases of matter

This thesis addresses whether it is possible to build a robust memory device for quantum information. Many schemes for fault-tolerant quantum information processing have been developed so far, one of which, called topological quantum computation, makes use of degrees of freedom that are inherently insensitive to local errors. However, this scheme is not so reliable against thermal errors. Other fault-tolerant schemes achieve better reliability through active error correction, but incur a substantial overhead cost. Thus, it is of practical importance and theoretical interest to design and assess fault-tolerant schemes that work well at finite temperature without active error correction.

In this thesis, a three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite temperature is possible, at least to some extent. When quantum information is encoded into a highly entangled ground state of this model and subjected to thermal errors, the errors remain easily correctable for a long time without any active intervention, because a macroscopic energy barrier keeps the errors well localized. As a result, stored quantum information can be retrieved faithfully for a memory time which grows exponentially with the square of the inverse temperature. In contrast, for previously known types of topological quantum storage in three or fewer spatial dimensions the memory time scales exponentially with the inverse temperature, rather than its square.

This spin model exhibits a previously unexpected topological quantum order, in which ground states are locally indistinguishable, pointlike excitations are immobile, and the immobility is not affected by small perturbations of the Hamiltonian. The degeneracy of the ground state, though also insensitive to perturbations, is a complicated number-theoretic function of the system size, and the system bifurcates into multiple noninteracting copies of itself under real-space renormalization group transformations. The degeneracy, the excitations, and the renormalization group flow can be analyzed using a framework that exploits the spin model's symmetry and some associated free resolutions of modules over polynomial algebras.

Cosmological consequences of dark matter interactions and vacuum fluctuations

This thesis is divided into two parts: interacting dark matter and fluctuations in cosmology. There is an incongruence between the properties that dark matter is expected to possess between the early universe and the late universe. Weakly-interacting dark matter yields the observed dark matter relic density and is consistent with large-scale structure formation; however, there is strong astrophysical evidence in favor of the idea that dark matter has large self-interactions. The first part of this thesis presents two models in which the nature of dark matter fundamentally changes as the universe evolves. In the first model, the dark matter mass and couplings depend on the value of a chameleonic scalar field that changes as the universe expands. In the second model, dark matter is charged under a hidden SU(N) gauge group and eventually undergoes confinement. These models introduce very different mechanisms to explain the separation between the physics relevant for freezeout and for small-scale dynamics.

As the universe continues to evolve, it will asymptote to a de Sitter vacuum phase. Since there is a finite temperature associated with de Sitter space, the universe is typically treated as a thermal system, subject to rare thermal fluctuations, such as Boltzmann brains. The second part of this thesis begins by attempting to escape this unacceptable situation within the context of known physics: vacuum instability induced by the Higgs field. The vacuum decay rate competes with the production rate of Boltzmann brains, and the cosmological measures that have a sufficiently low occurrence of Boltzmann brains are given more credence. Upon further investigation, however, there are certain situations in which de Sitter space settles into a quiescent vacuum with no fluctuations. This reasoning not only provides an escape from the Boltzmann brain problem, but it also implies that vacuum states do not uptunnel to higher-energy vacua and that perturbations do not decohere during slow-roll inflation, suggesting that eternal inflation is much less common than often supposed. Instead, decoherence occurs during reheating, so this analysis does not alter the conventional understanding of the origin of density fluctuations from primordial inflation.

Advanced density functional theory methods for materials science

In this work we chiefly deal with two broad classes of problems in computational materials science, determining the doping mechanism in a semiconductor and developing an extreme condition equation of state. While solving certain aspects of these questions is well-trodden ground, both require extending the reach of existing methods to fully answer them. Here we choose to build upon the framework of density functional theory (DFT) which provides an efficient means to investigate a system from a quantum mechanics description.

Zinc Phosphide (Zn₃P₂) could be the basis for cheap and highly efficient solar cells. Its use in this regard is limited by the difficulty in n-type doping the material. In an effort to understand the mechanism behind this, the energetics and electronic structure of intrinsic point defects in zinc phosphide are studied using generalized Kohn-Sham theory and utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. Novel 'perturbation extrapolation' is utilized to extend the use of the computationally expensive HSE functional to this large-scale defect system. According to calculations, the formation energy of charged phosphorus interstitial defects are very low in n-type Zn₃P₂ and act as 'electron sinks', nullifying the desired doping and lowering the fermi-level back towards the p-type regime. Going forward, this insight provides clues to fabricating useful zinc phosphide based devices. In addition, the methodology developed for this work can be applied to further doping studies in other systems.

Accurate determination of high pressure and temperature equations of state is fundamental in a variety of fields. However, it is often very difficult to cover a wide range of temperatures and pressures in an laboratory setting. Here we develop methods to determine a multi-phase equation of state for Ta through computation. The typical means of investigating thermodynamic properties is via ’classical’ molecular dynamics where the atomic motion is calculated from Newtonian mechanics with the electronic effects abstracted away into an interatomic potential function. For our purposes, a ’first principles’ approach such as DFT is useful as a classical potential is typically valid for only a portion of the phase diagram (i.e. whatever part it has been fit to). Furthermore, for extremes of temperature and pressure quantum effects become critical to accurately capture an equation of state and are very hard to capture in even complex model potentials. This requires extending the inherently zero temperature DFT to predict the finite temperature response of the system. Statistical modelling and thermodynamic integration is used to extend our results over all phases, as well as phase-coexistence regions which are at the limits of typical DFT validity. We deliver the most comprehensive and accurate equation of state that has been done for Ta. This work also lends insights that can be applied to further equation of state work in many other materials.

Wave interactions in periodic structures and periodic dielectric waveguides

This work is concerned with a general analysis of wave interactions in periodic structures and particularly periodic thin film dielectric waveguides.

The electromagnetic wave propagation in an asymmetric dielectric waveguide with a periodically perturbed surface is analyzed in terms of a Floquet mode solution. First order approximate analytical expressions for the space harmonics are obtained. The solution is used to analyze various applications: (1) phase matched second harmonic generation in periodically perturbed optical waveguides; (2) grating couplers and thin film filters; (3) Bragg reflection devices; (4) the calculation of the traveling wave interaction impedance for solid state and vacuum tube optical traveling wave amplifiers which utilize periodic dielectric waveguides. Some of these applications are of interest in the field of integrated optics.

A special emphasis is put on the analysis of traveling wave interaction between electrons and electromagnetic waves in various operation regimes. Interactions with a finite temperature electron beam at the collision-dominated, collisionless, and quantum regimes are analyzed in detail assuming a one-dimensional model and longitudinal coupling.

The analysis is used to examine the possibility of solid state traveling wave devices (amplifiers, modulators), and some monolithic structures of these devices are suggested, designed to operate at the submillimeter-far infrared frequency regime. The estimates of attainable traveling wave interaction gain are quite low (on the order of a few inverse centimeters). However, the possibility of attaining net gain with different materials, structures and operation condition is not ruled out.

The developed model is used to discuss the possibility and the theoretical limitations of high frequency (optical) operation of vacuum electron beam tube; and the relation to other electron-electromagnetic wave interaction effects (Smith-Purcell and Cerenkov radiation and the free electron laser) are pointed out. Finally, the case where the periodic structure is the natural crystal lattice is briefly discussed. The longitudinal component of optical space harmonics in the crystal is calculated and found to be of the order of magnitude of the macroscopic wave, and some comments are made on the possibility of coherent bremsstrahlung and distributed feedback lasers in single crystals.

Teoria quântica de campos para férmions interagentes no plano a temperatura e potencial químico finitos, na presença de um campo magnético externo oblíquo

Neste trabalho, os efeitos de um campo magnético oblíquo externo no modelo de Gross- Neveu (2+1)-dimensional, que inclui as componentes paralela e perpendicular do campo em relação ao sistema, são estudados no contexto da simetria quiral e discreta do modelo. Nosso principal interesse está nos efeitos deste campo sobre o diagrama de fase do sistema, onde também incluímos os efeitos combinados de temperatura e potencial químico. Os diagramas de fase são obtidos através do potencial efetivo a 1 loop para o modelo, derivado em primeira ordem na expansão 1=N. Transições de fase relevantes que podem ser estudadas através deste modelo são, por exemplo, metal-isolante em matéria condensada e na teoria quântica de campos de férmions planares em geral. A relação entre a transição de fase com quebra da simetria quiral e discreta e o surgimento de um gap (ou a presença de um valor esperado no vácuo do campo escalar diferente de zero), como função do campo magnético oblíquo, é analisada em detalhes.

Tópicos de teoria de campos com aplicações a condensados de Bose-Einstein

A tese de doutorado apresenta uma aplicação de técnicas de teoria de campos em um sistema da matéria condensada. Motivados por experimentos em gases atômicos, apresentamos um estudo sobre misturas binárias de gases atômicos na presença de uma interação do tipo Josephson. O foco principal é o estudo de um modelo de dois campos complexos não-relativisticos com simetria O(2). Esta simetria é quebrada por interações que produzem um desbalanço nas populações das duas espécies bosônicas. Estudamos o modelo na aproximação de campo médio mais flutuações gaussianas, usando o formalismo de teoria de campos a temperatura finita em tempo imaginário. Os resultados mostram que, num certo intervalo de temperaturas, as duas espécies bosônicas condensam à mesma temperatura crítica e a fase relativa do condensado é fixa, determinada pela fase do campo externo aplicado.

Modelo de Ginzburg-Landau a partir da teoria de campos a temperatura finita

Neste trabalho, utilizamos o formalismo de teorias quânticas de campos a temperatura finita, tal como desenvolvidas por Matsubara, aplicado a uma hamiltoniana de N campos escalares com autointeração quártica a N grande. Obtém-se uma expressão, na primeira aproximação quântica, para o coeficiente do termo quadrático da hamiltoniana ("massa quadrada"), renormalizado, como função da temperatura. A partir dela, estudamos o processo de quebra espontânea de simetria. Por outro lado, a mesma hamiltoniana é conhecida como modelo de Ginzburg-Landau na literatura de matéria condensada, e que permite o estudo de transições de fase em materiais ferromagnéticos. A temperatura é introduzida através do termo quadrático na hamiltoniana, de forma linear: é proporcional à diferença entre a variável de temperatura e a temperatura crítica. Tal modelo, porém, possui validade apenas na regi~ao de temperaturas próximas à criticalidade. Como resultado de nossos cálculos na teoria de campos a temperatura finita, observamos que, numa faixa de valores em torno da temperatura crítica, a massa quadrática pode ser aproximada por uma relação linear em relação à variável de temperatura. Isso evidencia a compatibilidade da abordagem de Ginzburg-Landau, na vizinhança da criticalidade, com respeito ao formalismo de campos a temperatura finita. Discutimos também os efeitos causados pela presença de um potencial químico no sistema.

Wetness loss prediction for a low pressure steam turbine using computational fluid dynamics

Two-phase computational fluid dynamics modelling is used to investigate the magnitude of different contributions to the wet steam losses in a three-stage model low pressure steam turbine. The thermodynamic losses (due to irreversible heat transfer across a finite temperature difference) and the kinematic relaxation losses (due to the frictional drag of the drops) are evaluated directly from the computational fluid dynamics simulation using a concept based on entropy production rates. The braking losses (due to the impact of large drops on the rotor) are investigated by a separate numerical prediction. The simulations show that in the present case, the dominant effect is the thermodynamic loss that accounts for over 90% of the wetness losses and that both the thermodynamic and the kinematic relaxation losses depend on the droplet diameter. The numerical results are brought into context with the well-known Baumann correlation, and a comparison with available measurement data in the literature is given. The ability of the numerical approach to predict the main wetness losses is confirmed, which permits the use of computational fluid dynamics for further studies on wetness loss correlations. © IMechE 2013 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.

DTADH and quantum critical phenomena caused by anisotropy and external magnetic field for spin-1/2 Heisenberg diamond chains

Using the transfer matrix renormalization group (TMRG) method, we study the connection between the first derivative of the thermal average of driving-term Hamiltonian (DTADH) and the trace of quantum critical behaviors at finite temperatures. Connecting with the exact diagonalization method, we give the phase diagrams and analyze the properties of each phase for both the ferromagnetic and anti-ferromagnetic frustrated J(3) anisotropy diamond chain models. The finite-temperature scaling behaviors near the critical regions are also investigated. Further, we show the critical behaviors driven by external magnetic field, analyze the formation of the 1/3 magnetic plateau and the influence of different interactions on those critical points for both the ferrimagnetic and anti-ferromagnetic distorted diamond chains.