501 research outputs found
A Novel Approach for Korteweg-de Vries Equation of Fractional Order
In this study, the localfractional variational iterationmethod (LFVIM) and the localfractional series expansion method (LFSEM) are utilized to obtain approximate solutions for Korteweg-de Vries equation (KdVE) within local fractionalderivative operators (LFDOs). The efficiency of the considered methods is illustrated by some examples. The results reveal that the suggested algorithms are very effective and simple and can be applied for linear and nonlinear problems in mathematical physics
Towards a solution of the closure problem for convective atmospheric boundary-layer turbulence
We consider the closure problem for turbulence in the dry convective atmospheric boundary
layer (CBL). Transport in the CBL is carried by small scale eddies near the surface and large
plumes in the well mixed middle part up to the inversion that separates the CBL from the
stably stratified air above. An analytically tractable model based on a multivariate Delta-PDF
approach is developed. It is an extension of the model of Gryanik and Hartmann [1] (GH02)
that additionally includes a term for background turbulence. Thus an exact solution is derived
and all higher order moments (HOMs) are explained by second order moments, correlation
coefficients and the skewness. The solution provides a proof of the extended universality
hypothesis of GH02 which is the refinement of the Millionshchikov hypothesis (quasi-
normality of FOM). This refined hypothesis states that CBL turbulence can be considered as
result of a linear interpolation between the Gaussian and the very skewed turbulence regimes.
Although the extended universality hypothesis was confirmed by results of field
measurements, LES and DNS simulations (see e.g. [2-4]), several questions remained
unexplained. These are now answered by the new model including the reasons of the
universality of the functional form of the HOMs, the significant scatter of the values of the
coefficients and the source of the magic of the linear interpolation. Finally, the closures
61
predicted by the model are tested against measurements and LES data. Some of the other
issues of CBL turbulence, e.g. familiar kurtosis-skewness relationships and relation of area
coverage parameters of plumes (so called filling factors) with HOM will be discussed also
Local quenches in fracton field theory: non-causal dynamics and fractal excitation patterns
We study the out-of-equilibrium dynamics induced by a local perturbation in
fracton field theory. For the and -symmetric
free fractonic theories, we compute the time dynamics of several observables
such as the two-point Green function, condensate,
energy density, and the dipole momentum. The time-dependent considerations
highlight that the free fractonic theory breaks causality and exhibits
instantaneous signal propagation, even if an additional relativistic term is
included to enforce a speed limit in the system. For the theory in finite
volume, we show that the fracton wave front acquires fractal shape with
non-trivial Hausdorff dimension, and argue that this phenomenon cannot be
explained by a simple self-interference effect.Comment: v1: 25 pages, 7 figures; v2: 25 pages, 7 figures, references added,
minor correction
Fracton phases of matter
Fractons are a new type of quasiparticle which are immobile in isolation, but can often move by forming bound states. Fractons are found in a variety of physical settings, such as spin liquids and elasticity theory, and exhibit unusual phenomenology, such as gravitational physics and localization. The past several years have seen a surge of interest in these exotic particles, which have come to the forefront of modern condensed matter theory. In this review, we provide a broad treatment of fractons, ranging from pedagogical introductory material to discussions of recent advances in the field. We begin by demonstrating how the fracton phenomenon naturally arises as a consequence of higher moment conservation laws, often accompanied by the emergence of tensor gauge theories. We then provide a survey of fracton phases in spin models, along with the various tools used to characterize them, such as the foliation framework. We discuss in detail the manifestation of fracton physics in elasticity theory, as well as the connections of fractons with localization and gravitation. Finally, we provide an overview of some recently proposed platforms for fracton physics, such as Majorana islands and hole-doped antiferromagnets. We conclude with some open questions and an outlook on the field
Topics in Magnetohydrodynamics
To understand plasma physics intuitively one need to master the MHD behaviors. As sciences advance, gap between published textbooks and cutting-edge researches gradually develops. Connection from textbook knowledge to up-to-dated research results can often be tough. Review articles can help. This book contains eight topical review papers on MHD. For magnetically confined fusion one can find toroidal MHD theory for tokamaks, magnetic relaxation process in spheromaks, and the formation and stability of field-reversed configuration. In space plasma physics one can get solar spicules and X-ray jets physics, as well as general sub-fluid theory. For numerical methods one can find the implicit numerical methods for resistive MHD and the boundary control formalism. For low temperature plasma physics one can read theory for Newtonian and non-Newtonian fluids etc
Recommended from our members
ANOMALOUS TRANSPORT, QUASIPERIODICITY, AND MEASUREMENT INDUCED PHASE TRANSITIONS
With the advent of the noisy-intermediate scale quantum (NISQ) era quantum computers are increasingly becoming a reality of the near future. Though universal computation still seems daunting, a great part of the excitement is about using quantum simulators to solve fundamental problems in fields ranging from quantum gravity to quantum many-body systems. This so-called second quantum revolution rests on two pillars. First, the ability to have precise control over experimental degrees of freedom is crucial for the realization of NISQ devices. Significant progress in the control and manipulation of qubits, atoms, and ions, as well as their interactions, has not only allowed for emulation of diverse range of physical systems but has also led to realization of quantum systems in non-conventional settings such as systems out-of-equilibrium, driven by oscillating fields, and with quasiperiodic (QP) modulation. These systems often show novel properties which not only provide an interesting testbed for NISQ devices but also an opportunity to exploit them for further development of quantum computing devices. Second, the study of dynamics of quantum information in quantum systems is essential for understanding and designing better quantum computers. In addition to their practical application as resource for quantum computation, quantum information has also become an essential element for our understanding of various physical problems, such as thermalization of isolated quantum many-body systems. This interplay between quantum information and computation, and quantum many-body systems is only expected to increase with time. In this thesis, we explore these topics in two parts, corresponding respectively to the two pillars mentioned above. In the first part, we study effects of quasiperiodicity on many-body quantum systems in low dimensions. QP systems are aperiodic but deterministic, so their behavior differs from that of clean systems and disordered ones as well. Moreover, these systems can be conveniently realized in an experimental setting where it is easier to isolate them from external decoherence. %Recent advancement in experimental techniques has made it easier to design and probe quantum systems with quasi-periodic modulations. We start with the easy-plane regime of the XXZ spin chain and show that the well-known fractal behavior of the spin Drude weight implies the divergence of the low-frequency conductivity for generic values of anisotropy. We tie this to the quasi-periodic structure in the Bethe ansatz solution resulting in different species of quasiparticles getting activated along the time evolution in a quasi-periodic pattern. We then study quantum critical systems under generic quasi-periodic modulations using real-space renormalization group (RSRG) procedure. In 1d, we show that the system flows to a new fixed point with the couplings following a discrete aperiodic sequence which allows us to analytically calculate the critical properties. We dub these new classes of quasi-periodic fixed points infinite-quasiperiodicity fixed points in line with the infinite-randomness fixed point observed in random quantum systems. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains. The RSRG is not analytically tractable in 2d, but numerically implementing it for the 2d quasi-periodic -state quantum Potts model, we find that it is well controlled and becomes exact in the asymptotic limit. The critical behavior is shown to be largely independent of and is controlled by an infinite-quasiperiodicity fixed point. We also provide a heuristic argument for the correlation length exponent and the scaling of the energy gap. Moving on to the second part, we study monitored quantum circuits which have recently emerged as a powerful platform for exploring the dynamics of quantum information and errors in quantum systems. Unitary evolution generates entanglement between distant particles of the system. The dynamics of entanglement has been successfully studied by replacing the Hamiltonian evolution with random quantum circuits. Recently, the robustness of unitary evolution\u27s ability to protect the entanglement against external projective measurements has received much attention. Entanglement is also a resource for quantum information, so its stability is directly related to the stability of a quantum computer against external noises. It has been observed that, in absence of any symmetry, there is a measurement induced phase transition (MIPT) in the behavior of bipartite entanglement that goes from volume law to area law as we tune the rate of measurements. Here we focus on monitored quantum circuits with U(1) symmetry which leads to the presence of a conserved charge density. These diffusive hydrodynamic modes scramble very differently than non-symmetric modes and we find that in addition to the entanglement transition, there is another transition \textit{inside} the volume phase which we call a ``charge sharpening\u27\u27 transition. The sharpening transition is a transition in the ability/inability of the measurements to detect the global charge of the system. We study this sharpening transition in a variety of settings, including an effective field theory that predicts the transition to be in a modified Kosterlitz-Thouless universality class. We provide various numerical evidence to back our predictions
- …