### Browsing by Department "Topological Quantum Fluids"

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Item 3He Universe 2020(SPRINGER/PLENUM PUBLISHERS, 2021-01) Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsThe latest news from 3He Universe are presented together with the extended map of the Universe.Item Acoustic Metric and Planck Constants(MAIK Nauka - Interperiodica, 2023-04) Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsBased on Akama–Diakonov (AD) theory of emergent tetrads, it was suggested that one can introduce two Planck constants,(Foemula Presented.), which are the parameters of the corresponding components of Minkowski metric, (Formula Presented.). In the Akama–Diakonov theory, the interval ds is dimensionless, as a result the metric elements and thus the Planck constants have nonzero dimensions. The Planck constant (Formula Presented.) has dimension of time, and the Planck constant (Formula Presented.) has dimension of length. It is natural to compare (Formula Presented.) with the Planck length lP. However, this connection remains an open question, because the microscopic (trans-Planckian) physics of the quantum vacuum is not known. Here we study this question using the effective gravity emerging for sound wave quanta (phonons) in superfluid Bose liquid, where the microscopic physics is known, and the elements of the effective acoustic metric are determined by the parameters of the Bose liquid. Since the acoustic interval is dimensionless, one may introduce the effective “acoustic Planck constants”. The acoustic Planck constant (Formula Presented.) has dimension of length and is on the order of the interatomic distance. This supports the scenario in which (Formula Presented.) ~ lP. We also use the acoustic metric for consideration of dependence of (Formula Presented.) on the Hubble parameter in expanding Universe.Item Big bang as a topological quantum phase transition(American Physical Society, 2022-04-15) Klinkhamer, F. R.; Volovik, G. E.; Karlsruhe Institute of Technology; Topological Quantum Fluids; Department of Applied PhysicsIt has been argued that a particular type of quantum-vacuum variable q can provide a solution to the main cosmological constant problem and possibly also give a cold-dark-matter component. We now show that the same q field may suggest a new interpretation of the big bang, namely as a quantum phase transition between topologically inequivalent vacua. These two vacua are characterized by the equilibrium values q=±q0, and there is a kink-type solution q(t) interpolating between q=-q0 for t→-∞ and q=+q0 for t→∞, with conformal symmetry for q=0 at t=0.Item Comment to the CPT-symmetic Universe(MAIK NAUKA/INTERPERIODICA/SPRINGER, 2019-07-30) Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsItem Dimensional crossover of effective orbital dynamics in polar distorted He 3-A(2018-01-25) Nissinen, J.; Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsTopologically protected superfluid phases of He3 allow one to simulate many important aspects of relativistic quantum field theories and quantum gravity in condensed matter. Here we discuss a topological Lifshitz transition of the effective quantum vacuum in which the determinant of the tetrad field changes sign through a crossing to a vacuum state with a degenerate fermionic metric. Such a transition is realized in polar distorted superfluid He3-A in terms of the effective tetrad fields emerging in the vicinity of the superfluid gap nodes: The tetrads of the Weyl points in the chiral A-phase of He3 and the degenerate tetrad in the vicinity of a Dirac nodal line in the polar phase of He3. The continuous phase transition from the A-phase to the polar phase, i.e., the transition from the Weyl nodes to the Dirac nodal line and back, allows one to follow the behavior of the fermionic and bosonic effective actions when the sign of the tetrad determinant changes, and the effective chiral spacetime transforms to antichiral "anti-spacetime." This condensed matter realization demonstrates that while the original fermionic action is analytic across the transition, the effective action for the orbital degrees of freedom (pseudo-EM) fields and gravity have nonanalytic behavior. In particular, the action for the pseudo-EM field in the vacuum with Weyl fermions (A-phase) contains the modulus of the tetrad determinant. In the vacuum with the degenerate metric (polar phase) the nodal line is effectively a family of 2+1d Dirac fermion patches, which leads to a non-analytic (B2-E2)3/4 QED action in the vicinity of the Dirac line.Item Dimensionless Physics : Planck Constant as an Element of the Minkowski Metric(MAIK NAUKA/INTERPERIODICA, 2023-02) Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsDiakonov theory of quantum gravity, in which tetrads emerge as the bilinear combinations of the fermionic fields, suggests that in general relativity the metric may have dimension 2; i.e., [guv=1/[L]2. Several other approaches to quantum gravity, including the model of superplastic vacuum and BF-theories of gravity support this suggestion. The important consequence of such metric dimension is that all the diffeomorphism invariant quantities are dimensionless for any dimension of spacetime. These include the action S, interval s, cosmological constant Λ, scalar curvature R, scalar field Φ, etc. Here we are trying to further exploit the Diakonov idea, and consider the dimension of the Planck constant. The application of the Diakonov theory suggests that the Planck constant (Formula Presented.) is the parameter of the Minkowski metric. The Minkowski parameter (Formula Presented.) is invariant only under Lorentz transformations, and is not diffeomorphism invariant. As a result, the Planck constant (Formula Presented.) has the dimension of length. Whether this Planck constant length is related to the Planck length scale, is an open question. In principle there can be different Minkowski vacua with their own values of the parameter (Formula Presented.) Then in the thermal contact between the two vacua their temperatures obey the analog of the Tolman law: (Formula Presented.).Item Elasticity tetrads, mixed axial-gravitational anomalies, and (3+1)-d quantum Hall effect(American Physical Society, 2019-09-06) Nissinen, J.; Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsFor two-dimensional topological insulators, the integer and intrinsic (without external magnetic field) quantum Hall effect is described by the gauge anomalous (2+1)-dimensional [(2+1)-d] Chern-Simons (CS) response for the background gauge potential of the electromagnetic U(1) field. The Hall conductance is given by the quantized prefactor of the CS term, which is a momentum-space topological invariant. Here, we show that three-dimensional crystalline topological insulators with no other symmetries are described by a topological (3+1)-dimensional [(3+1)-d] mixed CS term. In addition to the electromagnetic U(1) gauge field, this term contains elasticity tetrad fields E-mu(a) (r, t) = partial derivative X-mu(a) (r, t) which are gradients of crystalline U(1) phase fields X-a (r, t) and describe the deformations of the crystal. For a crystal in three spatial dimensions a = 1, 2, 3 and the mixed axial-gravitational response contains three parameters protected by crystalline symmetries: the weak momentum-space topological invariants. The response of the Hall conductance to the deformations of the crystal is quantized in terms of these invariants. In the presence of dislocations, the anomalous (3+1)-d CS term describes the Callan-Harvey anomaly inflow mechanism. The response can be extended to all odd spatial dimensions. The elasticity tetrads, being the gradients of the lattice U(1) fields, have canonical dimension of inverse length. Similarly, if such tetrad fields enter general relativity, the metric becomes dimensionful, but the physical parameters, such as Newton's constant, the cosmological constant, and masses of particles, become dimensionless.Item Exceeding the Landau speed limit with topological Bogoliubov Fermi surfaces(American Physical Society, 2020-07-02) Autti, Samuli; Mäkinen, Jere; Rysti, Juho; Volovik, Grigory; Zavyalov, Vladislav; Eltsov, Vladimir; Department of Applied Physics; Topological Quantum FluidsA common property of topological systems is the appearance of topologically protected zero-energy excitations. In a superconductor or superfluid, such states set the critical velocity of dissipationless flow vcL, proposed by Landau, to zero. We check experimentally whether stable superflow is nevertheless possible in the polar phase of p-wave superfluid 3He, which features a Dirac node line in the energy spectrum of Bogoliubov quasiparticles. The fluid is driven by rotation of the whole cryostat, and superflow breakdown is seen as the appearance of single- or half-quantum vortices. Vortices are detected using the relaxation rate of a Bose-Einstein condensate of magnons, created within the fluid. The superflow in the polar phase is found to be stable up to a finite critical velocity vc≈0.2cm/s, despite the zero value of the Landau critical velocity. We suggest that the stability of the superflow above vcL but below vc is provided by the accumulation of the flow-induced quasiparticles into pockets in the momentum space, bounded by Bogoliubov Fermi surfaces. In the polar phase, this surface has nontrivial topology which includes two pseudo-Weyl points. Vortices forming above the critical velocity are strongly pinned in the confining matrix, used to stabilize the polar phase, and hence stable macroscopic superflow can be maintained even when the external drive is brought to zero.Item Fifty years of research at the Landau Institute for Theoretical Physics (on the 100th anniversary of the birth of IM Khalatnikov)(Turpion Ltd., 2019) Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsReviewing all the basic research performed at the Landau Institute for Theoretical Physics, Russian Academy of Sciences that has made a significant contribution to physics is an unrealistic task. Therefore, the discussion is restricted to only those studies that have directly affected the author's explorations for 50 years (1968-2018). IMKhalatnikov created a unique institution that brought together virtually all areas of theoretical physics of importance, thus opening vast opportunities for scientific collaboration. The Landau Institute's multidisciplinary environment was a significant driver of research.Item Gravity from Symmetry Breaking Phase Transition(SPRINGER/PLENUM PUBLISHERS, 2022-05) Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsThe paper is devoted to the memory of Dmitry Diakonov. We discuss gravity emerging in the fermionic vacuum as suggested by Diakonov 10 years ago in his paper “Towards lattice-regularized Quantum Gravity”. [1] Gravity emerges in the phase transition. The order parameter in this transition is the tetrad field eμa, which appears as the bilinear composite of the fermionic fields. The similar scenario of the symmetry breaking takes place in the B-phase of superfluid 3He, where the real part of the spin-triplet p-wave order parameter matrix Aai plays the role of the emerging tetrad (triad). In Diakonov theory this symmetry breaking gives 6 Nambu-Goldstone modes; 6 gauge bosons in the spin-connection fields, which absorb 6 NG modes and become massive gauge bosons; and 6 Higgs fields. In 3He-B, these Higgs collective modes correspond to 6 massive gravitons, while in the emerging general relativity the Higgs collective modes give rise to two massless gravitational waves.Item Lessons from topological superfluids(EDP SCIENCES, 2019-09-01) Eltsov, V. B.; Nissinen, J.; Volovik, G. E.; Department of Applied Physics; Topological Quantum FluidsAll realistic second order phase transitions are undergone at finite transition rate and are therefore non-adiabatic. In symmetry-breaking phase transitions the non-adiabatic processes, as predicted by Kibble and Zurek [1, 2], lead to the formation of topological defects (the so-called Kibble-Zurek mechanism). The exact nature of the resultingdefects depends on the detailed symmetry-breaking pattern.Item On the Dimension of Tetrads in the Effective Gravity(MAIK NAUKA/INTERPERIODICA/SPRINGER, 2020-04) Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsTwo different sources of emergent gravity lead to the inverse square of length dimension of metric field, [gμν] = 1/[l]2, as distinct from the conventional dimensionless metric, [gμν] = 1, for c = 1. In both scenarios all the physical quantities, which obey diffeomorphism invariance, such as the Newton constant, the scalar curvature, the cosmological constant, particle masses, fermionic and scalar bosonic fields, etc., are dimensionless.Item Painlevé–Gullstrand coordinates for Schwarzschild–de Sitter spacetime(Academic Press, 2023-02) Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsThe Painlevé–Gullstrand coordinates are extended to describe the black hole in the cosmological environment: the Schwarzschild–de Sitter black hole, which has two horizons. The extension is made using the Arnowitt–Deser–Misner formalism. In this extension, which describes the metric in the whole range of radial coordinates 0r0 are free falling towards the cosmological horizon. The existence of the stationary observer allows to determine the temperature of Hawking radiation, which is in agreement with Bousso and Hawking (1996). It is the red-shifted modification of the conventional Hawking temperature determined by the gravity at the horizon. We also consider the Painlevé–Gullstrand coordinates and their extension for such configurations as Schwarzschild–de Sitter white hole, where the sign of the shift function is everywhere positive; the black hole in the environment of the contracting de Sitter spacetime, where the sign of the shift function is everywhere negative; and the white hole in the contracting de Sitter spacetime, where the shift velocity changes sign at r=r0.Item Particle Creation: Schwinger + Unruh + Hawking(MAIK NAUKA/INTERPERIODICA, 2022-11) Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsWe discuss the interconnection between the Schwinger pair creation in electric field, Hawking radiation and particle creation in the Unruh effect. All three processes can be described in terms of the entropy and temperature. These thermodynamic like processes can be combined. We consider the combined process of creation of charged and electrically neutral particles in the electric field, which combine the Schwinger and Unruh effects. We also consider the creation of the charged black and white holes in electric field, which combines the Schwinger effect and the black hole entropy. The combined processes obey the sum rules for the entropy and for the inverse temperature. Some contributions to the entropy and to the temperature are negative, which reflects the quantum entanglement between the created objects.Item Polar Phase of Superfluid 3He(2018-03-01) Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsThe time reversal symmetric polar phase of the spin-triplet superfluid 3He has two types of Dirac nodal lines. In addition to the Dirac loop in the spectrum of the fermionic Bogoliubov quasiparticles in the momentum space (px, py, pz), the spectrum of bosons (magnons) has Dirac loop in the 3D space of parameters—the components of magnetic field (Hx,Hy,Hz). The bosonic Dirac system lives on the border between the type-I and type-II.Item Quantum Turbulence and Planckian Dissipation(MAIK NAUKA/INTERPERIODICA, 2022-04) Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsThe notion of the Planckian dissipation is extended to the system of the Caroli-de Gennes-Matricon discrete energy levels in the vortex core of superconductors and fermionic superfluids. In this extension, the Planck dissipation takes place when the relaxation time τ is comparable with the quantum Heisenberg time tH = s important. The anomalous spectral flow of the energy levels along the chiral branch of the Caroli-de Gennes-Matricon states becomes important in the super-Planckian region, i.e. when τ < ΔE. Second, the Planck dissipation separates the laminar flow of the superfluid liquid at τ < ΔE and the vortex turbulence regime at τ > ΔE.Item Spin Vortex Lattice in the Landau Vortex-free State of Rotating Superfluids(MAIK NAUKA/INTERPERIODICA/SPRINGER, 2020-05) Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsWe show that the Landau vortex-free state in rotating container may give rise to the lattice of spin vortices. We consider this effect on example of spin vortices in magnon Bose–Einstein condensate (the phase coherent spin precession) in the B-phase of superfluid 3He, and on example of spin vortices in the polar phase of 3He.Item String monopoles, string walls, vortex skyrmions, and nexus objects in the polar distorted B phase of 3He(American Physical Society, 2020-06-02) Volovik, Grigory; Zhang, Kuang; Topological Quantum Fluids; Department of Applied PhysicsThe composite cosmological objects—Kibble-Lazarides-Shafi (KLS) walls bounded by strings and cosmic strings terminated by Nambu monopoles—could be produced during the phase transitions in the early universe. Recent experiments in superfluid 3He reproduced the formation of the KLS domain walls, which opened the new arena for the detailed study of those objects in a human controlled system with different characteristic lengths. These composite defects are formed by two successive symmetry breaking phase transitions. In the first transition the strings are formed, then in the second transition the string becomes the termination line of the KLS wall. In the same manner, in the first transition monopoles are formed, and then in the second transition these monopoles become the termination points of strings. Here we show that in the vicinity of the second transition the composite defects can be described by relative homotopy groups. This is because there are two well-separated length scales involved, which give riseto two different classes of the degenerate vacuum states, R1 and R2, and the composite objects correspond to the nontrivial elements of the group πn(R1,R2). We discuss this on example of the so-called polar distorted B phase, which is formed in the two-step phase transition in liquid 3He distorted by aerogel. In this system the string monopoles terminate spin vortices with an even winding number, while KLS string walls terminate on half-quantum vortices. In the presence of magnetic field, vortex skyrmions are formed, and the string monopole transforms to the nexus. We also discuss the integer-valued topological invariants of those objects. Our consideration can be applied to the composite defects in other condensed matter and cosmological systems.Item Thermal Nieh-Yan anomaly in Weyl superfluids(American Physical Society, 2020-08-19) Nissinen, J.; Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsWe discuss the possibility of torsional Nieh-Yan anomaly of the type partial derivative(mu) (ej(5)(mu)) = gamma T-2 (T-a Lambda T-a) in Weyl superfluids, where T is the infrared (IR) temperature scale and T a is the effective or emergent torsion from the superfluid order parameter. As distinct from the dimensionful ultraviolet (UV) parameter Lambda(2) in the conventional torsional Nieh-Yan anomaly, the parameter gamma is dimensionless in canonical units. This suggests that such dimensionless parameter may be fundamental, being determined by the geometry, topology, and number of chiral quantum fields in the system. By comparing this to a Weyl superfluid with low-temperature corrections, TItem Topological Superfluids(Maik Nauka-Interperiodica Publishing, 2019-10-01) Volovik, G. E.; Topological Quantum Fluids; Department of Applied PhysicsThere are many topological faces of the superfluid phases of 3He. These superfluids contain various topological defects and textures. The momentum space topology of these superfluids is also nontrivial, as well as the topology in the combined (p, r) phase space, giving rise to topologically protected Dirac, Weyl, and Majorana fermions living in bulk, on the surface and within the topological objects. The nontrivial topology lead to different types of anomalies, which extended in many different directions the Landau–Khalatninkov theory of superfluidity.