251 research outputs found
Monopole magnetohydrodynamics on a plane: Magnetosonic waves and dynamo instability
No full textDeutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Narodowe Centrum Nauki http://dx.doi.org/10.13039/50110000428
Ma Huan (original author), Wan Ming (ed.) Ming chaoben " Yingya shenglan " jiaozh
No full textPtak Roderich. Ma Huan (original author), Wan Ming (ed.) Ming chaoben " Yingya shenglan " jiaozh. In: Archipel, volume 71, 2006. Autour de la peinture à Java. Volume II. pp. 240-244
Universal Probability Distribution for the Wave Function of a Quantum System Entangled with Its Environment
No full textA quantum system (with Hilbert space H1) entangled with its environment (with Hilbert space H2) is usually not attributed a wave function but only a reduced density matrix ρ1. Nevertheless, there is a precise way of attributing to it a random wave function ψ1, called its conditional wave function, whose probability distribution μ1 depends on the entangled wave function ψ∈H1⊗H2 in the Hilbert space of system and environment together. It also depends on a choice of orthonormal basis of H2 but in relevant cases, as we show, not very much. We prove several universality (or typicality) results about μ1, e.g., that if the environment is sufficiently large then for every orthonormal basis of H2, most entangled states ψ with given reduced density matrix ρ1 are such that μ1 is close to one of the so-called GAP (Gaussian adjusted projected) measures, GAP(ρ1). We also show that, for most entangled states ψ from a microcanonical subspace (spanned by the eigenvectors of the Hamiltonian with energies in a narrow interval [E,E+δE]) and most orthonormal bases of H2, μ1 is close to GAP(tr2ρmc) with ρmc the normalized projection to the microcanonical subspace. In particular, if the coupling between the system and the environment is weak, then μ1 is close to GAP(ρβ) with ρβ the canonical density matrix on H1 at inverse temperature β=β(E). This provides the mathematical justification of our claim in [J. Statist. Phys. 125:1193 (2006), http://arxiv.org/abs/quant-ph/0309021] that GAP measures describe the thermal equilibrium distribution of the wave function.Peer reviewe
Dynamical fractal and anomalous noise in a clean magnetic crystal
No full textFractals—objects with noninteger dimensions—occur in manifold settings and length scales in nature. In this work, we identify an emergent dynamical fractal in a disorder-free, stoichiometric, and three-dimensional magnetic crystal in thermodynamic equilibrium. The phenomenon is born from constraints on the dynamics of the magnetic monopole excitations in spin ice, which restrict them to move on the fractal. This observation explains the anomalous exponent found in magnetic noise experiments in the spin ice compound Dy2Ti2O7, and it resolves a long-standing puzzle about its rapidly diverging relaxation time. The capacity of spin ice to exhibit such notable phenomena suggests that there will be further unexpected discoveries in the cooperative dynamics of even simple topological many-body systems.Fil: Hallén, Jonathan N.. University of Cambridge; Reino UnidoFil: Grigera, Santiago Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Tennant, D. Alan. University of Tennessee; Estados UnidosFil: Castelnovo, Claudio. University of Cambridge; Reino UnidoFil: Moessner, Roderich. Max Planck Institute For The Physics Of Complex Systems; Alemani
Disorder in an exactly solvable quantum spin liquid
No full textWe investigate the properties of the Kitaev honeycomb model with both site dilution and exchange randomness. Embarking on this work, we review disorder in some strongly correlated electron systems, including spin-½ and spin-1 Heisenberg antiferromagnetic chains, two dimensional Heisenberg antiferromagnets, the cuprates and graphene. We outline some aspects of resonating valence bond phases, valence bond solids, spin liquids and quantum computation that are pertinent to an understanding of the Kitaev model. The properties of the Kitaev model without disorder are discussed and it is found to be a critical spin liquid, with algebraic correlations in two spin operators sigma^{alpha}_{i}sigma^{alpha}_{j}, where i and j are either end of a link of type alpha = x, y or z on the honeycomb lattice. The Kitaev model is exactly solvable and we show that this remains so in the presence of site dilution and exchange randomness. We find that vacancies bind a flux. In the gapped phase, a vacancy forms an effective paramagnetic moment. With two or more vacancies we describe the interaction of their effective moments and show that a finite density of vacancies leads to a divergent macroscopic susceptibility at small fields. In the gapless phase the effective moment has a susceptibility that is, to leading order at small fields, chi(h)~log(1/h). Interaction between the moments from two vacancies on opposite sublattices cuts off this divergence in susceptibility at a large but finite constant. Two vacancies on the same sublattice behave quite differently and we find the combined susceptibility is parametrically larger than that of an isolated vacancy, chi(h)sim [h(log(1/h))^{3/2}]^{-1}. We also investigate the effects of slowly varying, quenched disorder in exchange coupling. We demonstrate that this does not qualitatively affect the susceptibility but show that the heat capacity C ~ T^{2/z}, where z is a measure of the disorder and increases from one with increasing disorder strength
Theodor Fontane, Julius Roderich Benedix and the royal theater in Berlin
No full textTheodor Fontane, Julius Roderich Benedix und das königliche Schauspielhaus in BerlinHeike JantschnerDiese Arbeit beschäftigt sich mit Theodor Fontane als Theaterkritiker für die Vossische Zeitung und Julius Roderich als Lustspielautor. Die Kernfragen der Arbeit lauten: Wer war der heute kaum noch bekannte Roderich Benedix? Warum waren seine Werke zu seinen Lebzeiten und Jahrzehnte postum noch so beliebt auf deutschen Bühnen? Worin liegt der Grund für dessen Beliebtheit? Um diesen Fragen nachzugehen, werden Theodor Fontanes Theaterkritiken vom königlichen Schauspielhaus in Berlin allgemein betrachtet, daraufhin seine Kritiken über Benedix genau analysiert. Daraus ergab sich, dass Benedix zu den beliebtesten deutschen Bühnenautoren seiner Zeit zählte. Seine Motive, Figuren sowie seine Komik waren neben den damals aufkommenden französischen Lustspielen und später dem Naturalismus eine erfrischende, harmlose, deutsche Alternative.Theodor Fontane, Julius Roderich Benedix and the royal theater in BerlinHeike JantschnerThe present work deals with the combined analysis of Theodor Fontane as a theater critic and Julius Roderich Benedix as a comedy author, respectively. The core issues of this volume can be summarized as follows: Who was this today rarely known man called Roderich Benedix? Why was his work during his lifetime as well as over decades posthumous that famous on German scenes? To respond to these raised questions, the critics of Theodor Fontane during his work at the royal theater of Berlin were, first of all, examined on a general basis followed by a detailed analysis of his critics regarding Benedix. This leads to the conclusion that Benedix ranked among the most popular scene writers at that time. The motives, characters created by him as well as his inimitable comic were, beside the arising comics from France and the upcoming naturalism, refreshing, harmless alternatives made in Germany.vorgelegt von Heike JantschnerAbweichender Titel laut Übersetzung der Verfasserin/des VerfassersZsfassungen in dt. und engl. SpracheGraz, Univ., Masterarb., 2015 2084
Through the looking glass of unconventional topological phases and fractionalization
No full textEver since quantum mechanics and relativity appeared at the beginning of the 20th century, physics has been rocked to its foundations. Novel ideas and applications surged relentlessly from the minds of those brave enough to venture into the unknown new worlds revealed by the new sciences. This year marks the centenary of Heisenberg’s quantum mechanics, and the exploration has not waned; rather, the frontiers of our knowledge now extend beyond fundamental theories into the complex playground of symmetry, topology, and emergence. We are faced with the challenge of understanding and predicting the behavior of complex systems in which the interplay of all three is essential for explaining their unique phenomena. Amid such an insurmountable challenge, novel viewpoints and signatures can often guide us through this dense web of complexity. In this doctoral thesis, we explore distinct scenarios where the intertwining of symmetry and topology naturally leads to previously unexplored phenomena, and subtle signatures arise from the combination of old and new theoretical frameworks in the weak and strong coupling regimes. In part one, we study weakly interacting topological phases. In chapter 2, we introduce the idea of time-reversal invariant finite-size topology. We identify signatures of a higher-dimensional bulk topological phase within thin films and wires; we probe this via Wilson loop spectroscopy and electromagnetic responses. Chapter 3 deals with extending previously studied topological skyrmion phases to time-reversal invariant systems. A generalization of the time-reversal parity invariant corresponds to a bulk-boundary texture of the pseudo-spin degrees of freedom. Moreover, our skyrmion invariant is directly linked to a reduced entanglement spectrum with protected spectral flow. Part two of this thesis is dedicated to strongly interacting electrons, where the effective description is that of a network of spins displaying the unconventional physics of spin liquids. In chapter 4, we describe how fractionalization can be generalized in classical spin liquids to yield irrational magnetic moments of dilution clusters. These clusters act as gauge charges for the low-energy lattice gauge theory. Moreover, we show that for a higher-rank gauge theory, distinctive emergent non-decaying spin textures and interactions are hallmarks of the unusual topological magnet. Chapter 5 studies a fragile spin liquid in three dimensions, which displays fractionalization but no algebraically decaying correlations. We find that not only is the Heisenberg model disordered, but the Ising model is as well. Perturbing away, we find a special point where quantum fluctuations stabilize a Z_2 quantum spin liquid
Anomalous spin dynamics in low-dimension: superdiffusion, subdiffusion, and solitons
No full textIn Part I of this thesis we examine solitons – local, non-dissipative excitations – in the dynamics of spin systems.
We open, in Ch. 1, with a short account of the history of solitons, from their first observation, to the theories of shallow water and the Korteweg-De Vries model; their appearance in field theories like the sine-Gordon model; to the general description of integrable systems, such as the Toda lattice. We pay particular attention, of course, to solitons in spin models – especially those obtained by Ishimori in an integrable classical spin chain which bears his name.
In Ch. 2 we present our work which establishes the existence of solitons in non-integrable spin chains. We begin by constructing exact static solitons in the Heisenberg chain, which we connect to the static Ishimori solitons via an adiabatic interpolation. We then use this adiabatic transform to construct moving Heisenberg solitons, which show no sign of having a finite lifetime. We further show that the interactions of these solitons are remarkably similar to the integrable case, and we establish their presence in low temperature thermal states – which will have important consequences in Part II.
Ch. 3 considers a different set-up, where we study the dynamics of domain walls in anisotropic spin chains. Our work shows a striking co-existence of linear and non-linear phenomena – to wit, we show that the free propagation and subdiffusive spreading of domain walls can be captured by non-interacting, linear spin wave theory; but that these domain walls are unstable to decay via the emission of topological solitons.
In Part II we will show how the solitons we have discovered play a hydrodynamic role, and find that superdiffusion, far from being limited to the special cases where the model is integrable, may be observed in non-integrable spin chains for (arbitrarily) long times, at low – but non-zero – temperatures.
We will, however, preface this with a review of the literature on superdiffusion in integrable spin chains in Ch. 4.
Ch. 5 presents our work on the existence of superdiffusion in non-integrable spin chains – with a particular focus, again, on the classical Heisenberg chain. We show that the Heisenberg chain exhibits long-lived superdiffusion of spin – with a striking scaling collapse of the correlation function onto the KPZ function across three decades of time at low temperature – but only ordinary diffusion of energy. We present an argument that explains this phenomenology in terms of the solitons we established in Part I.
Further, we examine how the time-scales and temperature-scales of superdiffusion depend on the degree of integrability breaking, by considering the model which interpolates between the Ishimori and Heisenberg chains (and which built the solitons of Ch. 2); and, furthermore, show examples of other non-integrable spin chains evincing the same spin superdiffusion at low temperatures.
We turn, in part III, to the opposite kind of anomalous dynamics – subdiffusion. We briefly survey this type of slow dynamics in Ch. 6, describing various mechanisms by which it can arise, including kinetic constraints, disorder, and higher-moment (e.g., the dipole moment) conservation of some charge density.
Ch. 7 contains our work on bond-disordered classical Heisenberg chains; the main contribution here is that we provide an interacting model with a continuously tune-able subdiffusive exponent, which we obtain analytically from a related, solvable phenomenological model. This also allows us to obtain the leading corrections to the asymptotic behaviour, clarifying the role of large sub-leading terms in hydrodynamic transport.
Now, Parts I – III of this thesis are concerned either with the structure of single excitations above the ground state – an effectively zero temperature regime – or the dynamics of the spins in thermal equilibrium, finding anomalous hydrodynamics both faster and slower than ordinary diffusion. In Part IV, however, we will forswear the canonical ensemble entirely.
In Ch. 8, we study the classical version of a boundary-driven quantum spin chain which was the subject of recent experiments by Google Quantum AI. We show that the observed dynamical regimes are not inherently quantum-mechanical, since the classical variant evinces the entire phenomenology observed in the quantum experiments. Moreover, we show that the classical chain is analytically tractable, and that, depending on the degree of anisotropy, either ballistic transport, subdiffusion, or localisation may be found.
We then go beyond the direct comparison with the quantum version and introduce quenched random couplings to the classical model. We find, most strikingly, that the ballistic transport regime survives, so long as the disorder is not strong enough to completely sever the chain. We further show how, if we do allow for very strong disorder, different subdiffusive exponents may be obtained.
In Ch. 9, we address the consequences of non-reciprocal interactions – in essence, an evasion of Newton’s third law – in periodically driven systems. This question emerges from the spin dynamics studied in the previous parts of this thesis because one of the main numerical methods we have used to calculate the time evolution is, intrinsically, a non-reciprocal periodic drive. Whilst Floquet theory – the study of periodically-driven Hamiltonian systems – is by now a well-developed field, non-reciprocal systems cannot be described by any Hamiltonian, time-dependent or static, and so the techniques of Floquet theory do not, a priori, apply. The high-frequency regime of Floquet systems typically features long-lived meta-stable (prethermal) states, which has allowed the techniques of Floquet-engineering to produce novel prethermal phases of matter which have no equilibrium counterpart – but the theorem which establishes the prethermal plateau explicitly uses the Hamiltonian formalism.
Nevertheless, by combining the ingredients of non-reciprocity and periodic driving in the context of many-body spin dynamics, we uncover a new class of long-lived prethermal states – independently of dimensionality, support of interactions, or lattice geometry – indicating that non-reciprocal systems may offer a propitious arena to generate new material properties via Floquet-engineering
Nonlinear waves in random lattices: localization and spreading
No full textHeterogeneity in lattice potentials (like random or quasiperiodic) can localize linear, non-interacting waves and halt their propagation. Nonlinearity induces wave interactions, enabling energy exchange and leading to chaotic dynamics. Understanding the interplay between the two is one of the topical problems of modern wave physics. In particular, one questions whether nonlinearity destroys localization and revives wave propagation, whether thresholds in wave energy/norm exist, and what the resulting wave transport mechanisms and characteristics are. Despite remarkable progress in the field, the answers to these questions remain controversial and no general agreement is currently achieved.
This thesis aims at resolving some of the controversies in the framework of nonlinear dynamics and computational physics. Following common practice, basic lattice models (discrete Klein-Gordon and nonlinear Schroedinger equations) were chosen to study the problem analytically and numerically. In the disordered linear case all eigenstates of such lattices are spatially localized manifesting Anderson localization, while nonlinearity couples them, enabling energy exchange and chaotic dynamics. For the first time we present a comprehensive picture of different subdiffusive spreading regimes and self-trapping phenomena, explain the underlying mechanisms and derive precise asymptotics of spreading. Moreover, we have successfully generalized the theory to models with spatially inhomogeneous nonlinearity, quasiperiodic potentials, higher lattice dimensions and arbitrary nonlinearity index.
Furthermore, we have revealed a remarkable similarity to the evolution of wave packets in the nonlinear diffusion equation. Finally, we have studied the limits of strong disorder and small nonlinearities to discover the probabilistic nature of Anderson localization in nonlinear disordered systems, demonstrating the finite probability of its destruction for arbitrarily small nonlinearity and exponentially small probability of its survival above a certain threshold in energy. Our findings give a new dimension to the theory of wave packet spreading in localizing environments, explain existing experimental results on matter and light waves dynamics in disordered and quasiperiodic lattice potentials, and offer experimentally testable predictions
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