arXiv subjects

Katherine Jones-Smith

Publications and source records attributed to Katherine Jones-Smith.

At least 19 recordsLinked to original sources

arXiv2023

Modified Newtonian Dynamics as an Alternative to the Planet Nine Hypothesis

A new class of Kuiper belt objects that lie beyond Neptune with semimajor axes greater than 250 astronomical units show orbital anomalies that have been interpreted as evidence for an undiscovered ninth planet. We show that a modified gravity theory known as MOND (Modified Newtonian Dynamics) provides an alternative explanation for the anomalies using the well-established secular approximation. We predict that the major axes of the orbits will be aligned with the direction towards the galactic center and that the orbits cluster in phase space, in agreement with observations of Kuiper belt objects from the new class. Thus MOND, which can explain galactic rotation without invoking dark matter, might also be observable in the outer solar system.

gr-qc↗

arXiv2018

The Radial Acceleration Relation and a Magnetostatic Analogy in Quasilinear MOND

Recently a remarkable relation has been demonstrated between the observed radial acceleration in disk galaxies and the acceleration predicted on the basis of baryonic matter alone. Here we study this relation within the framework of the modified gravity model MOND. The field equations of MOND automatically imply the radial acceleration relation for spherically symmetric galaxies, but for disk galaxies deviations from the relation are expected. Here we investigate whether these deviations are of sufficient magnitude to bring MOND into conflict with the observed relation. In the quasilinear formulation of MOND, to calculate the gravitational field of a given distribution of matter, an intermediate step is to calculate the "pristine field", which is a simple nonlinear function of the Newtonian field corresponding to the same distribution of matter. Hence, to the extent that the quasilinear gravitational field is approximately equal to the pristine field, the radial acceleration relation will be satisfied. We show that the difference between the quasilinear and pristine fields obeys the equations of magnetostatics, the curl of the pristine field serves as the source for the difference in the two fields, much as currents serve as sources for the magnetic field. Using the magnetostatic analogy we numerically study the difference between the pristine and quasilinear fields for simple model galaxies with a Gaussian profile. Our principal finding is that the difference between the fields is small compared to the observational uncertainties and that quasilinear MOND is therefore compatible with the observed radial acceleration relation.

astro-ph.GA↗

arXiv2018

Contact interactions and Kronig-Penney Models in Hermitian and PT-symmetric Quantum Mechanics

The delta function potential is a simple model of zero-range contact interaction in one dimension. The Kronig-Penney model is a one-dimensional periodic array of delta functions that models the energy bands in a crystal. Here we investigate contact interactions that generalize the delta function potential and corresponding generalizations of the Kronig-Penney model within conventional and parity-time symmetric quantum mechanics (PTQM). In conventional quantum mechanics we determine the most general contact interaction compatible with self-adjointness; in PTQM we consider interactions that are symmetric under the combined transformation PT. In both cases we find that the most general interaction has four independent real parameters; depending on the parameter values the interaction can support more bound states than the conventional delta function. In the PT case the two bound state energies can be both real or a complex conjugate pair, with the transition corresponding to the breaking of PT-symmetry. The scattering states for the PT case are also found to exhibit spontaneous breaking of PT-symmetry. We investigate the energy bands when the generalized contact interactions are repeated periodically in space in one dimension. In the Hermitian case we find that the two bound states result in two narrow bands generically separated by a gap. These bands intersect at a single point in the Brillouin zone as the interaction parameters are varied. Near the intersection the bands form a massless Dirac cone. In the PT-symmetric case, as the parameters of the contact interaction are varied the two bound state bands undergo a PT-symmetry breaking transition wherein the two band energies go from being real to being a complex conjugate pair. The PT-symmetric Kronig-Penney model provides a simple soluble example of the transition which has the same form as in other models of PT-symmetric crystals.

quant-ph↗

arXiv2018

The Effect of Forcing on Vacuum Radiation

Vacuum radiation has been the subject of theoretical study in both cosmology and condensed matter physics for many decades. Recently there has been impressive progress in experimental realizations as well. Here we study vacuum radiation when a field mode is driven both parametrically and by a classical source. We find that in the Heisenberg picture the field operators of the mode undergo a Bogolyubov transformation combined with a displacement, in the Schrödinger picture the oscillator evolves from the vacuum to a squeezed coherent state. Whereas the Bogolyubov transformation is the same as would be obtained if only the parametric drive were applied the displacement is determined by both the parametric drive and the force. If the force is applied well after the parametric drive then the displacement is the same as would be obtained by the action of the force alone and it is essentially independent of $t_f$, the time lag between the application of the force and the parametric drive. If the force is applied well before the parametric drive the displacement is found to oscillate as a function of $t_f$. This behavior can be understood in terms of quantum interference. A rich variety of behavior is observed for intermediate values of $t_f$. The oscillations can turn off smoothly or grow dramatically and decrease depending on strength of the parametric drive and force and the durations for which they are applied. The displacement depends only on the Fourier component of the force at a single resonant frequency when the forcing and the parametric drive are well separated in time. However for a weak parametric drive that is applied at the same time as the force we show that the displacement responds to a broad range of frequencies of the force spectrum. Implications of our findings for experiments are briefly discussed.

quant-ph↗

arXiv2017

Exploring extra dimensions with scalar waves

This paper provides a pedagogical introduction to the physics of extra dimensions focussing on the ADD, Randall-Sundrum and DGP models. In each of these models, the familiar particles and fields of the standard model are assumed to be confined to a four dimensional space-time called the brane; the brane is a slice through a higher dimensional space-time called the bulk. The geometry of the ADD, Randall-Sundrum and DGP space-times is described and the relation between Randall-Sundrum and Anti-de-Sitter space-time is explained. The necessary differential geometry background is introduced in an appendix that presumes no greater mathematical preparation than multivariable calculus. The ordinary wave equation and the Klein-Gordon equation are briefly reviewed followed by an analysis of the propagation of scalar waves in the bulk in all three extra-dimensional models. We also calculate the scalar field produced by a static point source located on the brane for all three models. For the ADD and Randall-Sundrum models at large distances the field looks like that of a point source in four space-time dimensions but at short distances it crosses over to a form appropriate to the higher dimensional space-time. For the DGP model the field has the higher dimensional form at long distances rather than short. The scalar field results provide qualitative insights into the corresponding behavior of gravitational fields. In particular the explanation within the ADD and Randall-Sundrum model of the weakness of gravity compared to other forces is discussed as are the implications of the two models for colliders and other experiments.

gr-qc↗

arXiv2017

An Electrostatic Analogy for Symmetron Gravity

The symmetron model is a scalar-tensor theory of gravity with a screening mechanism that suppresses the effect of the symmetron field at high densities characteristic of the solar system and laboratory scales but allows it to act with gravitational strength at low density on the cosmological scale. We elucidate the screening mechanism by showing that in the quasi-static Newtonian limit there are precise analogies between symmetron gravity and electrostatics for both strong and weak screening. For strong screening we find that large dense bodies behave in a manner analogous to perfect conductors in electrostatics. Based on this analogy we find that the symmetron field exhibits a lightning rod effect wherein the field gradients are enhanced near the ends of pointed or elongated objects. An ellipsoid placed in a uniform symmetron gradient is shown to experience a torque. By symmetry there is no gravitational torque in this case. Hence this effect unmasks the symmetron and might serve as the basis for future laboratory experiments. The symmetron force between a point mass and a large dense body includes a component corresponding to the interaction of the point mass with its image in the larger body. None of these effects have counterparts in the Newtonian limit of Einstein gravity. We discuss the similarities between symmetron gravity and the chameleon model as well as the differences between the two.

gr-qc↗

arXiv2017

An analysis of the LIGO discovery based on Introductory Physics

Binary black hole mergers are analyzed using concepts from introductory physics. Drawing upon Newtonian mechanics, dimensional considerations, and analogies between gravitational and electromagnetic waves, we are able to explain the principal features of LIGO's data and make order of magnitude estimates of key parameters of the event by inspection of the data. Our estimates of the black hole masses, the distance to the event, the initial separation of the pair, and the stupendous total amount of energy radiated are all in good agreement with the best fit values of these parameters obtained by the LIGO-VIRGO collaboration.

gr-qc↗

arXiv2017

The particle in a box in PT quantum mechanics and an electromagnetic analog

In PT quantum mechanics a fundamental principle of quantum mechanics, that the Hamiltonian must be hermitian, is replaced by another set of requirements, including notably symmetry under PT, where P denotes parity and T denotes time reversal. Here we study the role of boundary conditions in PT quantum mechanics by constructing a simple model that is the PT symmetric analog of a particle in a box. The model has the usual particle in a box Hamiltonian but boundary conditions that respect PT symmetry rather than hermiticity. We find that for a broad class of PT-symmetric boundary conditions the model respects the condition of unbroken PT-symmetry, namely that the Hamiltonian and the symmetry operator PT have simultaneous eigenfunctions, implying that the energy eigenvalues are real. We also find that the Hamiltonian is self-adjoint under the PT inner product. Thus we obtain a simple soluble model that fulfils all the requirements of PT quantum mechanics. In the second part of this paper we formulate a variational principle for PT quantum mechanics that is the analog of the textbook Rayleigh-Ritz principle. Finally we consider electromagnetic analogs of the PT-symmetric particle in a box. We show that the isolated particle in a box may be realized as a Fabry-Perot cavity between an absorbing medium and its conjugate gain medium. Coupling the cavity to an external continuum of incoming and outgoing states turns the energy levels of the box into sharp resonances. Remarkably we find that the resonances have a Breit-Wigner lineshape in transmission and a Fano lineshape in reflection; by contrast in the corresponding hermitian case the lineshapes always have a Breit-Wigner form in both transmission and reflection.

quant-ph↗

arXiv2014

Hofstadter's Cocoon

Hofstadter showed that the energy levels of electrons on a lattice plotted as a function of magnetic field form an beautiful structure now referred to as "Hofstadter's butterfly". We study a non-Hermitian continuation of Hofstadter's model; as the non-Hermiticity parameter $g$ increases past a sequence of critical values the eigenvalues successively go complex in a sequence of "double-pitchfork bifurcations" wherein pairs of real eigenvalues degenerate and then become complex conjugate pairs. The associated wavefunctions undergo a spontaneous symmetry breaking transition that we elucidate. Beyond the transition a plot of the real parts of the eigenvalues against magnetic field resembles the Hofstadter butterfly; a plot of the imaginary parts plotted against magnetic fields forms an intricate structure that we call the Hofstadter cocoon. The symmetries of the cocoon are described. Hatano and Nelson have studied a non-Hermitian continuation of the Anderson model of localization that has close parallels to the model studied here. The relationship of our work to that of Hatano and Nelson and to PT transitions studied in PT quantum mechanics is discussed.

quant-ph↗

arXiv2014

Relativistic Non-Hermitian Quantum Mechanics

We develop relativistic wave equations in the framework of the new non-hermitian ${\cal PT}$ quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of ${\cal PT}$-symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that in particular the mass matrix be Hermitian also allows for models that have no counterpart in conventional quantum mechanics. For example it is well-known that a quartet of Weyl spinors coupled by a Hermitian mass matrix reduces to two independent Dirac fermions; here we show that the same quartet of Weyl spinors, when coupled by a non-Hermitian but $\cal{PT}$ symmetric mass matrix, describes a single relativistic particle that can have massless dispersion relation even though the mass matrix is non-zero.The ${\cal PT}$-generalized Dirac equation is also Lorentz invariant, unitary in time, and CPT respecting, even though as a non-interacting theory it violates ${\cal P}$ and ${\cal T}$ individually. The relativistic wave equations are reformulated as canonical fermionic field theories to facilitate the study of interactions, and are shown to maintain many of the canonical structures from Hermitian field theory, but with new and interesting new possibilities permitted by the non-hermiticity parameter $m_2$.

hep-th↗

arXiv2013

Vector Models in PT Quantum Mechanics

We present two examples of non-Hermitian Hamiltonians which consist of an unperturbed part plus a perturbation that behaves like a vector, in the framework of PT quantum mechanics. The first example is a generalization of the recent work by Bender and Kalveks, wherein the E2 algebra was examined; here we consider the E3 algebra representing a particle on a sphere, and identify the critical value of coupling constant which marks the transition from real to imaginary eigenvalues. Next we analyze a model with SO(3) symmetry, and in the process extend the application of the Wigner-Eckart theorem to a non-Hermitian setting.

quant-ph↗

arXiv2013

A 'Dysonization' Scheme for Identifying Particles and Quasi-Particles Using Non-Hermitian Quantum Mechanics

In 1956 Dyson analyzed the low-energy excitations of a ferromagnet using a Hamiltonian that was non-Hermitian with respect to the standard inner product. This allowed for a facile rendering of these excitations (known as spin waves) as weakly interacting bosonic quasi-particles. More than 50 years later, we have the full denouement of non-Hermitian quantum mechanics formalism at our disposal when considering Dyson's work, both technically and contextually. Here we recast Dyson's work on ferromagnets explicitly in terms of two inner products, with respect to which the Hamiltonian is always self-adjoint, if not manifestly "Hermitian". Then we extend his scheme to doped antiferromagnets described by the t-J model, in hopes of shedding light on the physics of high-temperature superconductivity.

quant-ph↗

arXiv2012

Detecting Chameleon Dark Energy via Electrostatic Analogy

The late-time accelerated expansion of the universe could be caused by a scalar field that is screened on small scales, as in chameleon or symmetron scenarios. We present an analogy between thin shell configurations of such scalar fields and electrostatics, which allows calculation of the field profile for general extended bodies. Interestingly, the field demonstrates a `lightning rod' effect, where it becomes enhanced near the ends of a pointy or elongated object. Drawing from this correspondence, we show that non-spherical test bodies immersed in a background field will experience a net torque caused by the scalar field. This effect, with no counterpart in the gravitational case, can be potentially tested in future experiments.

astro-ph.CO↗

arXiv2011

Chameleon Effects on Small Scale Structure and the Baryonic Jeans Mass

In the framework of Newtonian cosmology or general relativity it is simple to derive a mass scale below which collapsed structures are relatively devoid of baryons. We examine how the inclusion of a chameleon scalar field affects this baryonic Jeans mass, bearing in mind both the canonical case of a gravitational-strength coupling between the scalar field and matter, as well as the strong coupling regime wherein the coupling is very large. We find that baryon effects persist down to smaller scales in a chameleon theory than they do in ordinary general relativity, especially in the case of strong coupling. Several potentially observable consequences of this are identified.

astro-ph.CO↗

arXiv2010

A New Class of non-Hermitian Quantum Hamiltonians with PT Symmetry

In a remarkable development Bender and coworkers have shown that it is possible to formulate quantum mechanics consistently even if the Hamiltonian and other observables are not Hermitian. Their formulation, dubbed PT quantum mechanics, replaces hermiticity by another set of requirements, notably that the Hamiltonian should be invariant under the discrete symmetry PT, where P denotes parity and T denotes time reversal. All prior work has focused on the case that time reversal is even (T^2 = 1). We generalize the formalism to the case of odd time reversal (T^2 = -1). We discover an analogue of Kramer's theorem for PT quantum mechanics, present a prototypical example of a PT quantum system with odd time reversal, and discuss potential applications of the formalism. Odd time reversal symmetry applies to fermionic systems including quarks and leptons and a plethora of models in nuclear, atomic and condensed matter physics. PT quantum mechanics makes it possible to enlarge the set of possible Hamiltonians that physicists could deploy to describe fundamental physics beyond the standard model or for the effective description of condensed matter phenomena.

hep-th↗

arXiv2010

Probing the Gravitational Wave Signature from Cosmic Phase Transitions at Different Scales

We present a new signature by which to one could potentially discriminate between a spectrum of gravitational radiation generated by a self-ordering scalar field vs that of inflation, specifically a comparison of the magnitude of a flat spectrum at frequencies probed by future direct detection experiments to the magnitude of a possible polarization signal in the Cosmic Microwave Background (CMB) radiation. In the process we clarify several issues related to the proper calculation of such modes, focusing on the effect of post-horizon-crossing evolution.

astro-ph.CO↗

arXiv2010

Aharonov-Bohm Radiation

A solenoid oscillating in vacuum will pair produce charged particles due to the Aharonov-Bohm (AB) interaction. We calculate the radiation pattern and power emitted for charged scalar particles. We extend the solenoid analysis to cosmic strings, and find enhanced radiation from cusps and kinks on loops. We argue by analogy with the electromagnetic AB interaction that cosmic strings should emit photons due to the gravitational AB interaction of fields in the conical spacetime of a cosmic string. We calculate the emission from a kink and find that it is of similar order as emission from a cusp, but kinks are vastly more numerous than cusps and may provide a more interesting observational signature.

hep-th↗

arXiv2009

Implications of Broken Symmetry for Superhorizon Conservation Theorems in Cosmology

Inflation produces super-horizon sized perturbations that ultimately return within the horizon and are thought to form the seeds of all observed large scale structure in the Universe. But inflationary predictions can only be compared with present day observations if, as conventional wisdom dictates, they remain unpolluted by subsequent sub-horizon causal physical processes and therefore remain immune from the vicissitudes of unknown universal dynamics in the intervening period. Here we demonstrate that conventional wisdom need not be correct, and as a result cosmological signatures arising from intervening unknown non-inflationary processes may confuse the interpretation of observational data today.

astro-ph.CO↗