scholarly journals Quasinormal modes in charged fluids at complex momentum

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Aron Jansen ◽  
Christiana Pantelidou
Keyword(s):  
Quasinormal Modes ◽  
Quantitative Agreement ◽  
Dispersion Relations ◽  
Radius Of Convergence ◽  
Complex Frequency ◽  
Branch Points ◽  
Charged Fluids ◽  
Hydrodynamic Modes ◽  
Momentum Plane ◽  
The One

Abstract We investigate the convergence of relativistic hydrodynamics in charged fluids, within the framework of holography. On the one hand, we consider the analyticity properties of the dispersion relations of the hydrodynamic modes on the complex frequency and momentum plane and on the other hand, we perform a perturbative expansion of the dispersion relations in small momenta to a very high order. We see that the locations of the branch points extracted using the first approach are in good quantitative agreement with the radius of convergence extracted perturbatively. We see that for different values of the charge, different types of pole collisions set the radius of convergence. The latter turns out to be finite in the neutral case for all hydrodynamic modes, while it goes to zero at extremality for the shear and sound modes. Furthermore, we also establish the phenomenon of pole-skipping for the Reissner-Nordström black hole, and we find that the value of the momentum for which this phenomenon occurs need not be within the radius of convergence of hydrodynamics.

scholarly journals Convergence of hydrodynamic modes: insights from kinetic theory and holography

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Michal P. Heller ◽  
Alexandre Serantes ◽  
Michal Spalinski ◽  
Viktor Svensson ◽  
Benjamin Withers
Keyword(s):  
Kinetic Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Dispersion Relations ◽  
Radius Of Convergence ◽  
Hydrodynamic Dispersion ◽  
Hydrodynamic Modes ◽  
Complex Singularities ◽  
Relaxation Time Approximation ◽  
New Feature

We study the mechanisms setting the radius of convergence of hydrodynamic dispersion relations in kinetic theory in the relaxation time approximation. This introduces a quali\-tatively new feature with respect to holography: a nonhydrodynamic sector represented by a branch cut in the retarded Green's function. In contrast with existing holographic examples, we find that the radius of convergence in the shear channel is set by a collision of the hydrodynamic pole with a branch point. In the sound channel it is set by a pole-pole collision on a non-principal sheet of the Green's function. More generally, we examine the consequences of the Implicit Function Theorem in hydrodynamics and give a prescription to determine a set of points that necessarily includes all complex singularities of the dispersion relation. This may be used as a practical tool to assist in determining the radius of convergence of hydrodynamic dispersion relations.

scholarly journals A holographic superfluid symphony

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Daniel Areán ◽  
Matteo Baggioli ◽  
Sebastian Grieninger ◽  
Karl Landsteiner
Keyword(s):  
Constitutive Relations ◽  
Quasinormal Modes ◽  
Role Reversal ◽  
Hydrodynamic Theory ◽  
Hydrodynamic Dispersion ◽  
Complex Frequency ◽  
Hydrodynamic Modes ◽  
Weakly Coupled ◽  
Reversal Phenomenon ◽  
Theory Framework

Abstract We study the hydrodynamic excitations of backreacted holographic superfluids by computing the full set of quasinormal modes (QNMs) at finite momentum and matching them to the existing hydrodynamic theory of superfluids. Additionally, we analyze the behavior of the low-energy excitations in real frequency and complex momentum, going beyond the standard QNM picture. Finally, we carry out a novel type of study of the model by computing the support of the hydrodynamic modes across the phase diagram. We achieve this by determining the support of the corresponding QNMs on the different operators in the dual theory, both in complex frequency and complex momentum space. From the support, we are able to reconstruct the hydrodynamic dispersion relations using the hydrodynamic constitutive relations. Our analysis rules out a role-reversal phenomenon between first and second sound in this model, contrary to results obtained in a weakly coupled field theory framework.

scholarly journals Magnetophonons & type-B Goldstones from hydrodynamics to holography

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Matteo Baggioli ◽  
Sebastian Grieninger ◽  
Li Li
Keyword(s):  
Magnetic Field ◽  
2D Materials ◽  
Goldstone Boson ◽  
Quasinormal Modes ◽  
Effective Field ◽  
Zero Magnetic Field ◽  
Type B ◽  
Hydrodynamic Modes ◽  
Pinning Mechanism ◽  
The Magnetic Field

Abstract We perform a detailed analysis of a large class of effective holographic models with broken translations at finite charge density and magnetic field. We exhaustively discuss the dispersion relations of the hydrodynamic modes at zero magnetic field and successfully match them to the predictions from charged hydrodynamics. At finite magnetic field, we identify the presence of an expected type-B Goldstone boson Re[ω] ∼ k2, known as magnetophonon and its gapped partner — the magnetoplasmon. We discuss their properties in relation to the effective field theory and hydrodynamics expectations. Finally, we compute the optical conductivities and the quasinormal modes at finite magnetic field. We observe that the pinning frequency of the magneto-resonance peak increases with the magnetic field, in agreement with experimental data on certain 2D materials, revealing the quantum nature of the holographic pinning mechanism.

scholarly journals Generalized Kramers–Kronig relations and sum rules for moments and powers of degenerate four wave mixing susceptibility

2021 ◽  
Author(s):  
Jarkko J. Saarinen
Keyword(s):  
Sum Rules ◽  
Terahertz Spectroscopy ◽  
Theoretical Models ◽  
Present Theory ◽  
Four Wave Mixing ◽  
Dispersion Relations ◽  
Nonlinear Susceptibility ◽  
Complex Frequency ◽  
Wave Mixing ◽  
Degenerate Four Wave Mixing

AbstractGeneralized Kramers–Kronig (K–K) type dispersion relations and sum rules are derived in the static limit for the moments of the degenerate four wave mixing susceptibility. The degenerate nonlinear susceptibility is different from a typical use of the conventional K–K dispersion relations, which assume absence of complex poles of a function in the upper half of complex frequency plane, whereas degenerate susceptibility has simultaneous poles in both half planes. In the derivation of the generalized K–K relations the poles and their order are taken into account by utilization of the theorem of residues. The conventional K–K relations can be used to estimate the real and imaginary parts of the second and higher powers of the susceptibility as the effect of the poles is reduced due to a faster convergence of the dispersion relations. The present theory is directly applicable to higher order susceptibilities and can be used in testing of theoretical models describing the degenerate four wave mixing susceptibility in nonlinear optical and terahertz spectroscopy.

Dynamics of Tubular Cantilevers Conveying Fluid

1970 ◽  
Vol 12 (2) ◽  
pp. 85-103 ◽  
Author(s):  
M. P. Paidoussis
Keyword(s):  
Quantitative Agreement ◽  
Dynamical Behaviour ◽  
Oscillatory Instability ◽  
Complex Frequency ◽  
Buckling Instability ◽  
Gravity Forces ◽  
Stability Maps ◽  
Conditions Of Stability ◽  
Conveying Fluid ◽  
Flow Velocities

In Part 1 a general theory is presented to account for the small, free, lateral motions of a vertical, uniform, tubular cantilever conveying fluid, with the free end being either below the clamped one (‘hanging’ cantilever) or above it (‘standing’ cantilever). Gravity forces are not considered to be negligible. It is shown that, when the velocity of the fluid exceeds a certain value, the cantilever in all cases becomes subject to oscillatory instability. In the case of hanging cantilevers buckling instability does not occur. Standing cantilevers, on the other hand, may buckle under their own weight; it is shown that in some cases flow (within a certain range of flow velocities) may render stable a system which would buckle in the absence of flow. Extensive complex frequency calculations were conducted to illuminate the dynamical behaviour of the system with increasing flow. The conditions of stability have also been extensively calculated and stability maps constructed. It is shown that dissipative forces may have either a stabilizing or a destabilizing effect on the system, partly depending on the magnitude of these forces themselves. The experiments described in Part 2 were designed to illustrate the dynamical behaviour of vertical tubular cantilevers conveying fluid. The experiments were conducted with rubber tubes conveying either water or air. The tubes were either hanging down or standing upright. It was observed that for sufficiently high flow velocities both hanging and standing cantilevers become subject to oscillatory instability. It was also observed that standing cantilevers which would buckle under their own weight in the absence of flow, in some cases are rendered stable by flow within a certain range of flow velocities. Qualitative and quantitative agreement between theory and experiment was satisfactorily good.

scholarly journals DENSITY RESULTS FOR SPECIALIZATION SETS OF GALOIS COVERS

2019 ◽  
pp. 1-42
Author(s):  
Joachim König ◽  
François Legrand
Keyword(s):  
Hyperelliptic Curves ◽  
Branch Points ◽  
Abc Conjecture ◽  
Galois Cover ◽  
Quadratic Twists ◽  
Large Genus ◽  
Galois Covers ◽  
The One ◽  
Almost All ◽  
Global Principle

We provide evidence for this conclusion: given a finite Galois cover $f:X\rightarrow \mathbb{P}_{\mathbb{Q}}^{1}$ of group $G$ , almost all (in a density sense) realizations of $G$ over $\mathbb{Q}$ do not occur as specializations of $f$ . We show that this holds if the number of branch points of $f$ is sufficiently large, under the abc-conjecture and, possibly, the lower bound predicted by the Malle conjecture for the number of Galois extensions of $\mathbb{Q}$ of given group and bounded discriminant. This widely extends a result of Granville on the lack of $\mathbb{Q}$ -rational points on quadratic twists of hyperelliptic curves over $\mathbb{Q}$ with large genus, under the abc-conjecture (a diophantine reformulation of the case $G=\mathbb{Z}/2\mathbb{Z}$ of our result). As a further evidence, we exhibit a few finite groups $G$ for which the above conclusion holds unconditionally for almost all covers of $\mathbb{P}_{\mathbb{Q}}^{1}$ of group $G$ . We also introduce a local–global principle for specializations of Galois covers $f:X\rightarrow \mathbb{P}_{\mathbb{Q}}^{1}$ and show that it often fails if $f$ has abelian Galois group and sufficiently many branch points, under the abc-conjecture. On the one hand, such a local–global conclusion underscores the ‘smallness’ of the specialization set of a Galois cover of $\mathbb{P}_{\mathbb{Q}}^{1}$ . On the other hand, it allows to generate conditionally ‘many’ curves over $\mathbb{Q}$ failing the Hasse principle, thus generalizing a recent result of Clark and Watson devoted to the hyperelliptic case.

scholarly journals THERMAL FIELD THEORY IN A WIRE: APPLICATIONS OF THERMAL FIELD THEORY METHODS TO THE PROPAGATION OF PHOTONS IN A ONE-DIMENSIONAL PLASMA

2011 ◽  
Vol 26 (32) ◽  
pp. 5387-5402 ◽  
Author(s):  
JOSÉ F. NIEVES
Keyword(s):  
Field Theory ◽  
Thermal Field Theory ◽  
Thermal Field ◽  
Free Field ◽  
Dynamical Variable ◽  
Effective Field ◽  
Dispersion Relations ◽  
One Dimensional ◽  
Self Energy ◽  
The One

The Thermal Field Theory methods are applied to calculate the dispersion relation of the photon propagating modes in a strictly one-dimensional (1D) ideal plasma. The electrons are treated as a gas of particles that are confined to a 1D tube or wire, but are otherwise free to move, without reference to the electronic wave functions in the coordinates that are transverse to the idealized wire, or relying on any features of the electronic structure. The relevant photon dynamical variable is an effective field in which the two space coordinates that are transverse to the wire are collapsed. The appropriate expression for the photon free-field propagator in such a medium is obtained, the one-loop photon self-energy is calculated and the (longitudinal) dispersion relations are determined and studied in some detail. Analytic formulas for the dispersion relations are given for the case of a degenerate electron gas, and the results differ from the long-wavelength formula that is quoted in the literature for the strictly 1D plasma. The dispersion relations obtained resemble the linear form that is expected in realistic quasi-1D plasma systems for the entire range of the momentum, and which have been observed in this kind of system in recent experiments.

A neutron scattering study of spin dynamics in the one-dimensional paramagnet CsMnBr3

1984 ◽  
Vol 62 (11) ◽  
pp. 1132-1138 ◽  
Author(s):  
B. D. Gaulin ◽  
M. F. Collins
Keyword(s):  
Neutron Scattering ◽  
Spin Wave ◽  
Spin Dynamics ◽  
Quantitative Agreement ◽  
Generalized Langevin Equation ◽  
Heisenberg Antiferromagnet ◽  
One Dimensional ◽  
Truncation Scheme ◽  
Zone Centre ◽  
The One

CsMnBr3 is a quasi-one-dimensional Heisenberg antiferromagnet. We present results of the magnetic inelastic response of CsMnBr3 across the magnetic Brillouin zone by neutron scattering techniques. Well-defined spin-wave modes, characteristic of one-dimensional magnetic insulators, are found over most of the zone in the paramagnetic phase at 15 K. The zone centre response is not sharp, but peaks in the scattering function S(k, ω) are found. No excitation branch going to zero energy at zero wavevector is found. At small wavevectors there is a mode with energy 1.7 ± 0.2 meV and we use it to identify planar anisotropy in this system. The mid-zone response as a function of temperature is analyzed in terms of a generalized Langevin equation approach (Mori formulation) to the dynamics of the one-dimensional Heisenberg antiferromagnet. The theory contains no adjustable parameters. Our results are compared with two truncation schemes of the theory. We report qualitative agreement with the theories, including the observation of upwards renormalization of spin-wave energy with temperature. Quantitative agreement is less than good for either truncation scheme.

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