Condensed Matter

Quantum time crystals are systems characterised by spontaneously emerging periodic order in the time domain. A range of such phases has been reported. The concept has even been discussed in popular literature, and deservedly so: while the first speculation on a phase of broken time translation symmetry did not use the name "time crystal", it was later adopted from 1980's popular culture. For the physics community, however, the ultimate qualification of a new concept is its ability to provide predictions and insight. Confirming that time crystals manifest the basic dynamics of quantum mechanics is a necessary step in that direction. We study two adjacent quantum time crystals experimentally. The time crystals, realised by two magnon condensates in superfluid 3 He-B, exchange magnons leading to opposite-phase oscillations in their populations -- AC Josephson effect -- while the defining periodic motion remains phase coherent throughout the experiment.

From Feynman diagrams to tensor networks, diagrammatic representations of computations in quantum mechanics have catalysed progress in physics. These diagrams represent the underlying mathematical operations and aid physical interpretation, but cannot generally be computed with directly. In this paper we introduce the ZXH-calculus, a graphical language based on the ZX-calculus, that we use to represent and reason about many-body states entirely graphically. As a demonstration, we express the 1D AKLT state, a symmetry protected topological state, in the ZXH-calculus by developing a representation of spins higher than 1/2 within the calculus. By exploiting the simplifying power of the ZXH-calculus rules we show how this representation straightforwardly recovers two important properties, the existence of topologically protected edge states, and the non-vanishing of a string order parameter. We furthermore show how the AKLT matrix-product state representation can be recovered from our diagrams. In addition, we provide an alternative proof that the 2D AKLT state on a hexagonal lattice can be reduced to a graph state, demonstrating that it is a universal quantum computing resource. Our results show that the ZXH-calculus is a powerful language for representing and computing with physical states entirely graphically, paving the way to develop more efficient many-body algorithms.

We derive a theoretical expression to calculate the Drude plasma frequency ω p based on quantum mechanical time dependent perturbation theory. We show that in general ω 2 p should be replaced by a second rank tensor, the Drude tensor D , which we express in terms of products of the velocity expectation values integrated over the Fermi surface, and which is amiable to analytical and numerical evaluation. For the Sommerfeld's model of metals our expression yields the ubiquitous plasma frequency ω 2 p =4π n e e 2 / m e . The Drude tensor takes into account the geometry of the unit cell and may be calculated from first principles for isotropic as well as anisotropic metallic systems. We present results for the noble metals, Cu, Ag, and Au without stress and subject to isotropic and uniaxial strains, and we compare the results to those available from experiment.

It is shown that the oscillation method to study liquid viscosity of [1-3,7-34], which is the basis of oscillation method to study crystallization and melting in multicomponent system, is based on incorrect consideration of one dimensional forced (constrained) )vibrations of plate in viscous liquid, because additional (apparent) mass of liquid and surface forces are incorrectly taken into account, and Archimedes force did not taken into account. It is shown that the vibrations cannot be one dimensional, and torsional vibrations need to be taken into account. It is shown also that the characteristics of vibrating system depend on time, the system has no isothermal conditions, the system cannot reach metastable conditions therefore one cannot observe homogeneous crystallization and melting, the results obtained with the use of the method are not reliable and incorrect.

It is shown that the oscillation method to study liquid viscosity of [1-3,7-34] is based on incorrect consideration of one dimensional forced (constrained) )vibrations of plate in viscous liquid, because additional (apparent) mass of liquid and surface forces are incorrectly taken into account, and Archimedes force did not taken into account. It is shown the vibrations cannot be one dimensional, and torsional vibrations need to be take into account, the results obtained with the use of the method are not reliable and incorrect.

It is shown that there is no proof of negativity of specific heat of the system placed in thermostat. It is proved that for the system of particles placed in the thermostat and interacting with each other via uniform potential energy the total energy is linear function of the temperature so the isobaric heat capacity is constant along the line of the zero pressure if the latter exists and the isobaric heat capacity is negative for value of the degree of uniformity of the potential energy negative and more than -2 and it is non-negative if otherwise.

It is shown that the functional form of the equation of state of [4-8] is not correct in general case.

This paper investigates an acoustic prism for continuous acoustic beam steering by a simple frequency sweep. This idea takes advantages of acoustic wave velocity shifting in metamaterials in the vicinity of local resonance. We apply this concept into the piezoelectric metamaterial consisting of host medium and piezoelectric LC shunt. Theoretical modeling and FEM simulations are carried out. It is shown that the phase velocity of acoustic wave changes dramatically in the vicinity of local resonance. The directions of acoustic wave can be adjusted continuously between 2 to 16 degrees by a simple sweep of the excitation frequency. Such an electro-mechanical coupling system has a feature of adjusting local resonance without altering the mechanical part of the system.

By solving the equations of ordinary and two-liquid hydrodynamics, we study the oscillatory modes in isotropic nonpolar dielectrics He I and He II in the presence of an alternating electric field E= E 0 i z sin( k 0 z− ω 0 t) . The electric field and oscillations of the density become "coupled," since the density gradient causes a spontaneous polarization P s , and the electric force contains the term ( P s ∇)E . The analysis shows that the field E changes the velocities of first and second sounds, propagating along E , by the formula u j ≈ c j + χ j E 2 0 (where j=1,2 , c j is the velocity of the j -th sound for E 0 =0 , and χ j is a constant). We have found that the field E jointly with a wave of the first (second) sound (ω,k) should create in He II hybrid acousto-electric (thermo-electric) density waves (ω+l ω 0 ,k+l k 0 ) , where l=±1,±2,… . The amplitudes of acousto-electric waves and the quantity | u 1 − c 1 | are negligibly small, but they should increase in the resonance way at definite ω and ω 0 . Apparently, the first resonance corresponds to the decay of a photon into two phonons with the transfer of a momentum to the whole liquid. Therefore, the spectrum of an electromagnetic signal should contain a narrow absorption line like that in the Mössbauer effect.

The transfer of topological concepts from the quantum world to classical mechanical and electronic systems has opened fundamentally new approaches to protected information transmission and wave guidance. A particularly promising technology are recently discovered topolectrical circuits that achieve robust electric signal transduction by mimicking edge currents in quantum Hall systems. In parallel, modern active matter research has shown how autonomous units driven by internal energy reservoirs can spontaneously self-organize into collective coherent dynamics. Here, we unify key ideas from these two previously disparate fields to develop design principles for active topolectrical circuits (ATCs) that can self-excite topologically protected global signal patterns. Building on a generic nonlinear oscillator representation, we demonstrate both theoretically and experimentally the emergence of self-organized protected edge states in ATCs. The good agreement between theory, simulations and experiment implies that ATCs can be realized in many different ways. Beyond topological protection, we also show how one can induce persistent localized bulk wave patterns by strategically placing defects in 2D lattice ATCs. These results lay the foundation for the practical implementation of autonomous electrical circuits with robust functionality in arbitrarily high dimensions.