One-form superfluids and magnetohydrodynamics

We use the framework of generalised global symmetries to study various hydrodynamic regimes of hot electromagnetism. We formulate the hydrodynamic theories with an unbroken or a spontaneously broken U(1) one-form symmetry. The latter of these describes a one-form superfluid, which is characterised by a vector Goldstone mode and a two-form superfluid velocity. Two special limits of this theory have been studied in detail: the string fluid limit where the U(1) one-form symmetry is partly restored, and the electric limit in which the symmetry is completely broken. The transport properties of these theories are investigated in depth by studying the constraints arising from the second law of thermodynamics and Onsager's relations at first order in derivatives. We also construct a hydrostatic effective action for the Goldstone modes in these theories and use it to characterise the space of all equilibrium configurations. To make explicit contact with hot electromagnetism, the traditional treatment of magnetohydrodynamics, where the electromagnetic photon is incorporated as dynamical degrees of freedom, is extended to include parity-violating contributions. We argue that the chemical potential and electric fields are not independently dynamical in magnetohydrodynamics, and illustrate how to eliminate these within the hydrodynamic derivative expansion using Maxwell's equations. Additionally, a new hydrodynamic theory of non-conducting, but polarised, plasmas is formulated, focusing primarily on the magnetically dominated sector. Finally, it is shown that the different limits of one-form superfluids formulated in terms of generalised global symmetries are exactly equivalent to magnetohydrodynamics and the hydrodynamics of non-conducting plasmas at the non-linear level.Comment: v3: 69 + 1 pages, 1 figure, added clarifications and appendix with discrete symmetries, to be published in JHE

COMPUTATIONAL RATIONAL DESIGN OF ELECTROCATALYSTS FOR ELECTROCHEMICAL AMMONIA AND HYDROGEN SYNTHESIS

The electrochemical hydrogen evolution reaction (HER) and nitrogen reduction reaction (NRR) offer fossil-fuel-free routes for hydrogen and ammonia synthesis, respectively. However, currently, both processes lack suitable electrocatalysts for practical applications. Thus, this dissertation focuses on the computational rational design of HER and NRR electrocatalysts. HER is most efficiently catalyzed by platinum (Pt), which is expensive. To reduce the catalyst cost, we investigate core-shell nanoparticles of inexpensive tungsten-carbide (WC) and Pt (WC@Pt). Using first-principles density functional theory (DFT) calculations, we compare the suitability of two WC phases, α-WC and β-WC as support materials for Pt overlayers. We dope WC with titanium and examine its effects on the thermodynamic stability and HER activity of WC and WC@Pt nanoparticles. We show that β-WC is more suited than α-WC for stabilizing Pt overlayers, and that moderate titanium doping of WC is an effective approach to stabilize β-WC and β-WC@Pt nanoparticles. Thereafter, we investigate molybdenum diselenide (MoSe2) for HER. The catalytic activity of MoSe2 is limited because most of its electrochemical surface area—the basal plane—is inert towards HER. To activate the basal plane, we examine the effect of doping MoSe2 with electron-rich transition metals (Mn, Fe, Co, and Ni). Our DFT studies show that all selected dopants improve HER thermodynamics on the basal plane. We also find that all selected transition-metal dopants promote the formation of HER active Se-vacancy sites in MoSe2. Overall, our studies show that transition-metal-doping of MoSe2 is an effective strategy to activate MoSe2 for HER. Finally, we investigate molybdenum disulfide (MoS2) for NRR. To overcome its low NRR activity and selectivity, we dope MoS2 with iron. With DFT calculations, we show that the formation of iron-doped edges is energetically preferred over undoped edges of MoS2. We show that catalytically active sulfur vacancies are more readily formed at iron-doped edges than at undoped edges of MoS2. We show that such defect-rich iron-doped edges can catalyze NRR at moderate cathodic potentials and we propose a new mechanism for NRR at these sites. Our studies show that iron-doping of MoS2 is a potentially viable strategy for producing inexpensive, active, and selective NRR electrocatalysts

Theory of non-Abelian superfluid dynamics

We write down a theory for non-Abelian superfluids with a partially broken (semisimple) Lie group. We adapt the off-shell formalism of hydrodynamics to superfluids and use it to comment on the superfluid transport compatible with the second law of thermodynamics. We find that the second law can be also used to derive the Josephson equation, which governs dynamics of the Goldstone modes. In the course of our analysis, we derive an alternate and mutually distinct parametrization of the recently proposed classification of hydrodynamic transport and generalize it to superfluids

A universal framework for hydrodynamics

In this thesis, we present a universal framework for hydrodynamics starting from the fundamental considerations of symmetries and the second law of thermodynamics, while allowing for additional gapless modes in the low-energy spectrum. Examples of such fluids include superfluids and fluids with surfaces. Typically, additional dynamical modes in hydrodynamics also need to be supplied with their own equations of motion by hand, like the Josephson equation for superfluids and the Young-Laplace equation for fluid surfaces. However, we argue that these equations can be derived within the hydrodynamic framework by a careful off-shell generalisation of the second law. This potentially provides a universal framework for a large class of hydrodynamic theories, based on their underlying symmetries and gapless modes. Motivated by this newly found universality, we present an all-order analysis of the second law of thermodynamics and propose a classification scheme for the allowed hydrodynamic transport, including arbitrary gapless modes, independent spin current, and background torsion. In the second half of this thesis, we look at the construction of null fluids which are a new viewpoint of Galilean fluids. These are essentially fluids coupled to spacetime backgrounds carrying a covariantly constant null isometry, but with additional constraints imposed on the background gauge field and affine connection to reproduce the correct Galilean degrees of freedom. We discuss the Galilean version of quantum anomalies and their effect on hydrodynamics. Finally, we follow our relativistic discussion to allow for arbitrary gapless modes in Galilean hydrodynamics and present a classification scheme for the second law abiding hydrodynamic transport at all orders in the derivative expansion. We apply these abstract ideas to review the theory of ordinary relativistic/Galilean hydrodynamics and provide novel constructions for relativistic/Galilean (non-Abelian) superfluid dynamics and surface transport. We also comment on the possible application to the theory of magnetohydrodynamics

Location estimation in a 3D environment using radio frequency identification tags

RFID tag location estimation in a 3D environment is investigated. The location of the tag with unknown coordinates can be estimated with certain accuracy. However, accuracy can be improved using the knowledge based on measurement of additional reference tags with known location. This thesis studies the mathematical formulation and practical realization of location sensing using RFID tags. Deviating from the standard use of RFID technology which employs one tag reader to identify the presence of tag, here multiple tag readers with known location are used to estimate the physical location of an individual tag, with/without the help of few reference tags with known locations. Mathematical model of this concept has been developed based on distance variations in terms of signal strength. Experimental approach with limited range passive tags has been carried out. Since the range of the RFID system was limited only to a few inches, signal strength variations were insignificant. Instead, time domain measurements with the help of an external antenna were conducted. The composite signal width including of the wake up signal of the interrogator, travel time between the interrogator and tag, and the tag\u27s response was measured and quantified. It was observed that the width of the signal was proportional to the distance between the tag reader and the tag. It was noticed that the use of four RFID tag readers yielded fairly accurate results to identify the location the tag based on the mathematical formulation developed here. Additionally, concept of trilateration has also been extended for tracking the tag of unknown location without the use of reference tags. Archival data set corresponding to all tag location due to four different tag readers was compiled. The unknown tag was probed with four tag readers and matching the data to the archival data set yielded unique and accurate results for its unknown location. It was demonstrated that both approaches were proved to be cost-effective techniques and estimation of the location of a specific tag has been achieved with sufficient accuracy

A Classification Model for Sensing Human Trust in Machines Using EEG and GSR

Today, intelligent machines \emph{interact and collaborate} with humans in a way that demands a greater level of trust between human and machine. A first step towards building intelligent machines that are capable of building and maintaining trust with humans is the design of a sensor that will enable machines to estimate human trust level in real-time. In this paper, two approaches for developing classifier-based empirical trust sensor models are presented that specifically use electroencephalography (EEG) and galvanic skin response (GSR) measurements. Human subject data collected from 45 participants is used for feature extraction, feature selection, classifier training, and model validation. The first approach considers a general set of psychophysiological features across all participants as the input variables and trains a classifier-based model for each participant, resulting in a trust sensor model based on the general feature set (i.e., a "general trust sensor model"). The second approach considers a customized feature set for each individual and trains a classifier-based model using that feature set, resulting in improved mean accuracy but at the expense of an increase in training time. This work represents the first use of real-time psychophysiological measurements for the development of a human trust sensor. Implications of the work, in the context of trust management algorithm design for intelligent machines, are also discussed.Comment: 20 page

Approximate higher-form symmetries, topological defects, and dynamical phase transitions

Higher-form symmetries are a valuable tool for classifying topological phases of matter. However, emergent higher-form symmetries in interacting many-body quantum systems are not typically exact due to the presence of topological defects. In this paper, we develop a systematic framework for building effective theories with approximate higher-form symmetries, i.e. higher-form symmetries that are weakly explicitly broken. We focus on a continuous U(1) q-form symmetry and study various patterns of symmetry breaking. This includes spontaneous or explicit breaking of higher-form symmetries, as well as pseudo-spontaneous symmetry breaking patterns where the higher-form symmetry is both spontaneously and explicitly broken. We uncover a web of dualities between such phases and highlight their role in describing the presence of dynamical higher-form vortices. In order to study the out-of-equilibrium dynamics of these phases of matter, we formulate respective hydrodynamic theories and study the spectra of excitations exhibiting higher-form charge relaxation and Goldstone relaxation effects. We show that our framework is able to describe various phase transitions due to proliferation of vortices or defects. This includes the melting transition in smectic crystals, the plasma phase transition from polarised gases to magnetohydrodynamics, the spin-ice transition, the superfluid to neutral fluid transition and the Meissner effect in superconductors, among many others

Schwinger-Keldysh effective field theory for stable and causal relativistic hydrodynamics

We construct stable and causal effective field theories (EFTs) for describing statistical fluctuations in relativistic diffusion and relativistic hydrodynamics. These EFTs are fully non-linear, including couplings to background sources, and enable us to compute n-point time-ordered correlation functions including the effects of statistical fluctuations. The EFTs we construct are inspired by the Maxwell-Cattaneo model of relativistic diffusion and M\"uller-Israel-Stewart model of relativistic hydrodynamics respectively, and have been derived using both the Martin-Siggia-Rose and Schwinger-Keldysh formalisms. The EFTs non-linearly realise the dynamical Kubo-Martin-Schwinger (KMS) symmetry, which ensures that n-point correlation functions and interactions in the theory satisfy the appropriate fluctuation-dissipation theorems. Since these EFTs typically admit ultraviolet sectors that are not fixed by the low-energy infrared symmetries, we find that they simultaneously admit multiple realisations of the dynamical KMS symmetry. We also comment on certain obstructions to including statistical fluctuations in the recently-proposed stable and causal Bemfica-Disconzi-Noronha-Kovtun model of relativistic hydrodynamics.Comment: 47+1 page