Részecskefizikai és Térelméleti Kutatócsoport
https://wigner.hu/hu
hu2019_Field Theory
https://wigner.hu/hu/node/1497
<span class="field field--name-title field--type-string field--label-hidden">2019_Field Theory</span>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><p><strong>Poisson-Lie analogues of spin Sutherland models.</strong> — Exactly solvable models of point particles moving along one dimension have been studied intensively for nearly 50 years, due to their diverse physical applications ranging from effective descriptions of solitons to supersymmetric Yang-Mills theories. These models involve rational, trigonometric or elliptic interaction potentials, and the `Sutherland models’ represent the trigonometric case. They have interesting extensions in which the interacting particles are coupled to internal, `spin’ degrees of freedom. In Ref. <a href="https://doi.org/10.1016/j.nuclphysb.2019.114807">[1]</a>, we constructed new generalizations of the spin Sutherland models by applying symplectic symmetry reduction to certain free systems that live on the Heisenberg double of an arbitrary compact simple Poisson-Lie group. The Hamiltonian structure of the reduced systems was fully described, and it was shown that the leading terms of the pertinent Poisson brackets and Hamiltonians reproduce the previously known spin Sutherland models. It turned out that an analytic continuation of the models associated with the unitary group U(n) reproduces models introduced earlier by Braden and Hone in a study of interacting solitons of affine Toda field theories. In another paper <a href="https://doi.org/10.1088/1361-6544/ab2d5e">[2]</a>, the Braden-Hone system of evolution equations was found to admit two distinct Hamiltonian descriptions, which are compatible in the sense that an arbitrary linear combination of the corresponding Poisson brackets is again a Poisson bracket, i.e., the system has a bi-Hamiltonian structure. The generalization of the bi-Hamiltonian structure to other compact Lie groups, as well as the quantization and applications of the new classical integrable systems will be explored in the future.</p>
<p><strong>Exotic entanglement entropy scaling.</strong> — Entanglement entropy has become a ubiquitous tools in the study many-body systems. In 1D systems it usually diverges logarithmically for critical systems, while it saturates to a finite value in non-critical systems. In Ref. <a href="https://doi.org/10.1088/1742-5468/ab38b6">[3]</a>, we studied the scaling of the entanglement and Rényi entropies in the ground state of long-range Kitaev chains with slowly decaying coupling strengths. We obtained that, under some circumstances, the entropy grows sublogarithmically with the length of the subsystem; this is the first translation-invariant state presented in the literature that has this type of entanglement scaling. Our result is based on the asymptotic behavior of a new class of Toeplitz determinants whose symbol does not lie within the application domain of the Strong Szegő Theorem or the Fisher-Hartwig conjecture.</p>
<p><strong>Short time asymptotics of quantum dynamics.</strong> — Dynamical evolution of systems with sparse Hamiltonians can always be recognized as continuous time quantum walks (CTQWs) on graphs. In Ref.<a href="https://doi.org/10.1103/PhysRevA.100.062320"> [4]</a>, we analyzed the short time asymptotics of CTQWs. In previous studies it was shown that for the classical diffusion process the short time asymptotics of the transition probabilities follow power laws whose exponents are given by the usual combinatorial distances of the nodes. Inspired by this result, we performed a similar analysis for CTQWs both in closed and open systems, including time-dependent couplings. For time-reversal symmetric coherent quantum evolutions, the short time asymptotics of the transition probabilities is completely determined by the topology of the underlying graph analogously to the classical case, but with a doubled power-law exponent. Moreover, this result is robust against the introduction of on-site potential terms. However, we showed that time-reversal symmetry breaking terms and non-coherent effects can significantly alter the short time asymptotics (see Figure 1.). Furthermore, we discussed in detail the relevance of our results for quantum evolutions on particular network topologies.</p>
<img alt="térelmélet" data-entity-type="file" data-entity-uuid="6ce13e67-65c7-4a91-8b3e-83865aa4bf6a" src="https://wigner.hu/sites/default/files/inline-images/terelmelet1.png" width="500" class="align-center" />
<p class="text-align-center"><em>Figure 1. Comparison of short-time asymptotics of arrival probabilities in time-reversal symmetric and chiral quantum walks on the graph depicted in the left lower corner of the figure.</em></p>
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<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://wigner.hu/hu/user/124" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">Pentek Csilla</span></span>
<span class="field field--name-created field--type-created field--label-hidden">k, 06/30/2020 - 10:48</span>
Tue, 30 Jun 2020 08:48:38 +0000Pentek Csilla1497 at https://wigner.hu2018_Particle Physics and Field Theory
https://wigner.hu/hu/node/1488
<span class="field field--name-title field--type-string field--label-hidden">2018_Particle Physics and Field Theory</span>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><h4><strong>2018</strong></h4>
<p><strong>Einstein-conformally coupled Standard Model.</strong> — We introduced and studied a classical field theoretical model, the so-called Einstein-conformally coupled Standard Model (EccSM), which is general relativistic and in which (according to the key idea above) the matter sector is coupled to gravity in a conformally invariant manner. We showed that, in this theory, in addition to the usual initial Big Bang singularity there might be a so-called Small Bang singularity, too (in which it is only the spacetime geometry is singular but all the matter field variables remain bounded), and that in the generic case Newton's gravitational constant yields an absolute upper bound for the magnitude of the Higgs field. Furthermore, the resulting rest masses of the fields depend on time, and although their time dependence can be neglected soon after their genesis, but about 10-27 seconds after the initial singularity (which is the characteristic time of the weak interactions) this time dependence could still in principle be shown up in the starting up particle physics processes.</p>
<p><strong>Noether currents for the Teukolsky master equation.</strong> — The Teukolsky master equation is an important wave equation that governs the evolution of the extreme spin weight components of the electromagnetic, linearized gravitational, neutrino and spin-3/2 fields in Kerr (i.e., rotating black hole) spacetime. For various purposes, e.g. for testing numerical simulations and for studying the decay properties of the mentioned fields, it is desirable to know conserved currents for this equation. However, the Teukolsky master equation does not follow from a Lagrangian, therefore the usual procedure, which is to apply Noether's theorem, is not suitable for finding conserved currents for it. By applying a less well-known variant of Noether's theorem, we showed that a pair of Teukolsky master equations with opposite spin weights does follow from a Lagrangian, and constructed conserved currents that correspond to the time translation and axial symmetries of the Kerr spacetime and to the scaling symmetry of the Teukolsky master equation. These currents involve two independent solutions of the Teukolsky master equation with opposite spin weights. We also introduced general definitions for the symmetries and conserved currents of boundary conditions of partial differential equations, extended Noether's theorem and its variant to them, and used this extension of the latter variant to construct conserved currents associated with the Sommerfeld boundary condition in the case of the Teukolsky master equation. Such boundary conserved currents are again useful for testing purposes in numerical simulations.</p>
<p><strong>Quantum Correlations in Many-Body Systems.</strong> — We studied various types of quantum correlations in many-body systems and field theories. One of these was entanglement negativity, which is a versatile measure of entanglement that has numerous applications in quantum information and in condensed matter theory. It can not only efficiently be computed in the Hilbert space dimension, but for Gaussian bosonic systems, one can compute the negativity efficiently in the number of modes. However, such an efficient computation does not carry over to the fermionic realm, the ultimate reason for this being that the partial transpose of a fermionic Gaussian state is no longer Gaussian. To provide a remedy for this state of affairs, we introduced efficiently computable and rigorous upper and lower bounds to the negativity, making use of techniques of semi-definite programming, building upon the Lagrangian formulation of fermionic linear optics, and exploiting suitable products of Gaussian operators. We also discussed examples in quantum many-body theory with applications in the study of topological properties at finite temperature.</p>
<p>Another investigated measure was the quantum Fisher information. We calculated the Fisher information quantity for different states of atomic ensembles in a magnetic field, see Fig. 1. The value of the Fisher information can signal nonclassicality, but it is also important from a metrological point of view. In particular we calculated precision bounds for estimating the gradient of the magnetic field based on the quantum Fisher information. We also considered a single atomic ensemble with an arbitrary density profile, where the atoms cannot be addressed individually, and which is a very relevant case for experiments.</p>
<p><img alt="Figure 1. Angular momentum components and their variances for various spin states for few particles are shown: (a) singlet state, (b) z-Dicke state, (c) state totally polarized in the y-direction, (d) x-Dicke state, (e) GHZ state. " data-entity-type="file" data-entity-uuid="462b178d-c110-4bc7-a23c-25f53e132147" src="https://wigner.hu/sites/default/files/inline-images/Zoltan%20Zimboras_%202018.jpg" /></p>
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<p><strong>Figure 1.</strong> Angular momentum components and their variances for various spin states for few particles are shown: (a) singlet state, (b) z-Dicke state, (c) state totally polarized in the y-direction, (d) x-Dicke state, (e) GHZ state. </p></div>
<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://wigner.hu/hu/user/124" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">Pentek Csilla</span></span>
<span class="field field--name-created field--type-created field--label-hidden">v, 06/16/2019 - 11:10</span>
Sun, 16 Jun 2019 09:10:22 +0000Pentek Csilla1488 at https://wigner.hu2017 - Particle Physics and Field Theory Research Group
https://wigner.hu/hu/node/943
<span class="field field--name-title field--type-string field--label-hidden">2017 - Particle Physics and Field Theory Research Group </span>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><h4><strong>2017</strong></h4>
<p><strong>Quantum physics: universal gate sets and measurements. </strong>— For numerous applications of quantum theory it is desirable to be able to apply arbitrary unitary operations on a given quantum system. However, in particular situations only a subset of unitary operations is easily accessible. This raises the question of what additional unitary gates should be added to a given gate-set in order to attain physical universality, i.e., to be able to perform arbitrary unitary transformation on the relevant system. We studied this problem for three paradigmatic cases of naturally occurring restricted gate-sets: particle-number preserving bosonic linear optics, particle-number preserving fermionic linear optics, and general (not necessarily particle-number preserving) fermionic linear optics. Using tools from group theory, we were able to classify, in each of these scenarios, what sets of gates are generated, if an additional gate is added to the set of allowed transformations. This allowed us to solve the universality problem completely for arbitrary number of particles and for arbitrary dimensions of the single-particle Hilbert space. We also attacked the problem of describing quantum measurements, we constructed a two-step dynamical model for selective measurements in quantum mechanics. The first step is the non-selective measurement or decoherence described by a semigroup of completely positive maps, which is given by the linear, deterministic first order Lindblad differential equation. The second step is a process from the resulted decohered state to a pure state, which is described by an effective non-linear `randomly chosen' toy model dynamics: the pure states arise as asymptotic fixed points, and their emergent probabilities are the relative volumes of their attractor regions.</p>
<p><strong>Integrable systems and quantum groups.</strong> — We have derived new integrable many-body models of Ruijsenaars--Schneider--van Diejen type by applying Hamiltonian reduction to the Heisenberg double of the Poisson--Lie group SU(2n), and clarified the global structure of the phase space for another model in the same family. We have also continued our study of describing algebraic structures that go beyond groups. In an earlier work, we have already studied a distinguished class of Hopf monads in monoidal bicategories. Hopf algebras and most of their known generalizations were shown to fit this class. Since then, however, some newer generalizations of Hopf algebras — so-called Hopf categories and Hopf polyads — appeared in the literature. In this year, we constructed a monoidal bicategory in which also these structures, as well as Turaev’s Hopf group algebras, can be regarded as Hopf monads. In order to describe quantum we constructed a two-step dynamical model for selective measurements in quantum mechanics.</p>
<p><strong>Gravitational theory: spinning binary black-hole systems.</strong> — The Lagrangian of the spinning binary system contains acceleration-dependent terms in some cases of spin supplementary condition (SSC). We constructed the nontrivial generalized Hamiltonian formalism with the high-order canonical moments proposed by Ostrogradsky and calculated the conserved quantities such as the energy and the magnitude of the orbital angular momentum for each SSC. Thus we computed the first integrals of the spinning dynamics and gave the perturbative radial and angle motion with the help of the generalized radial parameterization. Moreover, we defined the generalized Poisson brackets following the work of Yang and Hirschfelder and we have given the canonical structure of the spinning binary. Finally, we generalized the result of Kidder for the spinning waveform and for the dissipative part of relative motion during the gravitational radiation of each SSC (Fig. 1).</p>
<p><span><span><img alt="z1" data-entity-type="file" data-entity-uuid="7aa47ea9-51a9-4fc9-8734-75a7fc51b7ef" height="400" src="https://wigner.hu/sites/default/files/inline-images/zimbi01.png" width="600" /></span></span></p>
<p><strong>Figure 1. </strong>Dissipative quantities of the binary in the different spin supplementary conditions</p>
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<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://wigner.hu/hu/user/171" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">Werovszky Veronika</span></span>
<span class="field field--name-created field--type-created field--label-hidden">h, 08/06/2018 - 13:36</span>
Mon, 06 Aug 2018 11:36:27 +0000Werovszky Veronika943 at https://wigner.hu