Vortex Formations from Domain Wall Annihilations in Two-Component Bose-Einstein Condensates

We theoretically study the vortex formation from the collision of the domain walls in phase-separated two-component Bose-Einstein condensates. The collision process mimics the tachyon condensation for the annihilation of D-brane and anti-D-brane in string theory. A pair annihilation leaves the quantized vortices with superflow along their core, namely superflowing cosmic strings. It is revealed that the line density and the core size of the vortices depend on the initial distance between the walls.     

The AB Interface in Superfluid 3He as a Simulated Cosmological Brane

We present measurements of the transport of superfluid ³He quasiparticle excitations in the ballistic limit at temperatures well below T _c , and an interpretation of unexpected results as an experimental simulation of cosmological processes. Using a variable magnetic field profile we stabilize a layer of A phase across a cylinder of B phase, creating both an AB and a BA interface. These highly ordered interfaces may provide an ideal laboratory analogy for the branes and anti-branes of current cosmology. It has been suggested that brane interaction and annihilation are involved in inflation in the early Universe and leave behind topological defects such as cosmic strings. In our experiments we have annihilated our AB/BA branes by ramping down the magnetic field to remove the A phase layer. We then find that the quasiparticles face an extra impedance owing to defects left behind in the B phase texture. This is the first definitive observation of such a phenomenon.     

Effective Action Approach to Bose-Einstein Condensation of Ideal Gases

We present a short review of how the effective action formalism, well known in relativistic quantum field theory, can be used to discuss Bose-Einstein condensation of non-relativistic gases. This method lends itself very naturally to an interpretation of Bose-Einstein condensation in terms of symmetry breaking. It also allows for the definition of a very elegant regularization technique involving generalized ζ-functions. We show how this method can be used to recover the well known results for the free boson gas, as well as the charged boson gas in a constant magnetic field. A general criterion for interpreting Bose-Einstein condensation in terms of a phase transition with symmetry breaking is given. Finally we present an analysis of Bose-Einstein condensation in a harmonic oscillator confining potential trap, and show how the results of this simple model are in excellent agreement with experiment.     

Dependence of structure and properties of vacuum condensates of some metals and alloys on conditions of deposition

We present data on the relationship between the strength and hardness of vacuum condensates of aluminium, copper and Cu-Al alloys and the structure formed as a result of the combined effect of the main parameters of the deposition process (the rate of condensation, pressure, temperature, crucible material and substrate). The mechanical strength of the condensates is discussed from the viewpoint of their contribution to strengthening the compact grain structure, the initial dislocation density and the rate of accumulation during plastic deformation.We propose a formula which is convenient for numerical calculation and which relates the concentration of the element in the condensate to the composition of the evaporated binary alloy. We also present values for the thermodynamics activities of copper and aluminium in the melt, which were obtained by analysing the composition of the condensate at different stages of formation.New data are presented on the phase state of Cu-Al and Cu-Sn films which indicate a reduction of the solubility of aluminium in copper to 3–5 wt.% at 20–400°C, and we give data on the mutual diffusion coefficients D? in Cu-Al condensates, which exceed by 3–6 orders of magnitude the D? values of the massive analogues.     

Superfluid, Superconducting, and Magnetic Ordering in Mesoscopic Quantum Dots

The nature of superfluid, superconducting, and magnetic ordering is elucidated for mesoscopic systems in which the single-particle level spacing is much larger than both the temperature and the critical temperature of ordering. Ordering is defined as a spontaneous breaking of symmetry, the gauge invariance and time reversal being by definition symmetries broken in superfluidity (superconductivity) and magnetism contexts, respectively. Superfluidity and superconductivity are realized in thermodynamic equilibrium states with a nonintegral average number of particles and are accompanied by the spontaneous breaking of time homogeneity. In Fermi systems, two types of superfluidity and superconductivity are possible which are characterized by the presence of pair or single-particle condensates. The latter is remarkable in that spontaneous breaking of fundamental symmetries such as spatial 2 rotation and double time reversal takes place. Possible experiments on metallic nanoparticles and ultracold atomic gases in magnetic traps are discussed.     

Connection of Vortices Between Spatially Different Phases in Two-Component Bose-Einstein Condensates

We study interfacial topological defects called boojums, a vortex ending or a connecting point of two kinds of vortex cores, in rotating two-component Bose-Einstein condensates. First, we show that the boojum exists at a vortex ending that connects to the interface of the strongly phase-separated condensates. Next, we study various boojums appearing between two phases characterized by different vortex structures, where the intercomponent s-wave scattering lengths are spatially varied. Using three-dimensional simulations of the Gross-Pitaevskii equations, we reveal the detailed structure of the boojums by visualizing its density distribution and effective superflow vorticity.     

Quantized Massive Gauge Fields and Hole-Induced Spin Glass Mechanism in Underdoped Cuprates

We have discussed the restoration mechanism of the spontaneous symmetry breaking, C ₂ spatial symmetry breaking mechanism, and spin glass-like mechanism in high- T _c cuprates from the standpoint of field-theoretical formula. It is suggested strongly that quantized massive gauge fields, which contain effects of spin fluctuations, charge fluctuations, and phonons, might be mediating Cooper pairing in high- T _c cuprates.     

Bose–Einstein Condensates in 2D with Time-Periodic Scattering Length

We discuss two-dimensional Bose–Einstein Condensates (BEC) under timeperiodic variation of the scattering length. In particular we argue that for high-frequency variation there exist stable self-confined condensates without an external trap, when the do component of the scattering length is negative. Our resugts are based on a variational approximation, on direct averaging of the Gross–Pitaevskii equation and on numerical simulations.     

Bistability and macroscopic quantum coherence in BECs: the two cases of attractive and repulsive interactions

We consider Bose-Einstein condensates (BECs) in situations where the density undergoes a symmetry breaking, either in real space or in momentum space. This occurs for a suitable number of condensed atoms in a double well potential, obtained in real space for a BEC of lithium atoms by adding a standing wave light field to the trap potential, or in momentum space for rubidium atoms by Raman coupling two BECs in different magnetic states with two tilted light fields. Evidence of bistability results from the solution of the Gross-Pitaevskii equation. By second quantization, we show that the classical bistable situation is in fact a Schrödinger cat (SC) and we evaluate the macroscopic quantum coherence between the two SC states.     

Theories of Linear Response in BCS Superfluids and How They Meet Fundamental Constraints

We address the importance of symmetry and symmetry breaking on linear response theories of fermionic BCS superfluids. The linear response theory of a noninteracting Fermi gas is reviewed and several consistency constraints are verified. The challenge to formulate linear response theories of BCS superfluids consistent with density and spin conservation laws comes from the presence of a broken U(1)_EM symmetry associated with electromagnetism (EM) and we discuss two routes for circumventing this. The first route follows Nambu’s integral-equation approach for the EM vertex function, but this method is not specific for BCS superfluids. We focus on the second route based on a consistent-fluctuation-of-the order-parameter (CFOP) approach where the gauge transformation and the fluctuations of the order parameter are treated on equal footing. The CFOP approach allows one to explicitly verify several important constraints: The EM vertex satisfies not only a Ward identity which guarantees charge conservation but also a Q-limit Ward identity associated with the compressibility sum rule. In contrast, the spin degrees of freedom associated with another U(1) _z symmetry are not affected by the Cooper-pair condensation that breaks only the U(1)_EM symmetry. As a consequence the collective modes from the fluctuations of the order parameter only couple to the density response function but decouple from the spin response function, which reflects the different fates of the two U(1) symmetries in the superfluid phase. Our formulation lays the ground work for applications to more general theories of BCS-Bose Einstein Condensation (BEC) crossover both above and below T _c .     

Localization of the Relative Phase via Measurements

When two independently-prepared Bose-Einstein condensates are released from their corresponding traps, the absorption image of the overlapping clouds presents an interference pattern. Here we analyze a model introduced by Javanainen and Yoo (Phys. Rev. Lett. 76:161, 1996), who considered two atomic condensates described by plane waves propagating in opposite directions. We present an analytical argument for the measurement-induced breaking of the relative phase symmetry in this system, demonstrating how the phase gets localized after a large enough number of detection events.     

Annihilation of an AB/BA interface pair in superfluid helium-3 as a simulation of cosmological brane interaction

This study presents measurements of the transport of quasiparticle excitations in the B phase of superfluid 3He at temperatures below 0.2Tc. We find that creating and then removing a layer of A-phase superfluid leads to a measurable increase in the thermal impedance of the background B phase. This increase must be due to the survival of defects created as the AB and BA interfaces on either side of the A-phase layer annihilate. We speculate that a new type of defect may have been formed. The highly ordered A-B interface may be a good analogy for branes discussed in current cosmology. If so, these experiments may provide insight into how the annihilation of branes can lead to the formation of topological defects such as cosmic strings.     

Tables of the irreducible representations of the 17 two-dimensional space groups and their relevance to quantum mechanical eigenstates for surfaces and thin films

The theory of the determination of the irreducible representations of the two-dimensional space groups is briefly reviewed and then it is used to produce tables of these irreducible representations for each of the two-dimensional space groups. Additional degeneracies due to time-reversal symmetry are also identified. The rules for establishing the relationship between the two-dimensional space group for the (hkl) surface of a crystal and the three-dimensional space group for a bulk specimen of the same crystalline material are also given.     

Dimerization Triggered Magnetoelectric Coupling Effect and Magnetic Anisotropy in Organic Ternary Crystals

Developing a new universal strategy to design all organic ferromagnets or multiferroics with satisfactory properties always remains challenging. In this work, ternary charge transfer crystals are fabricated to realize organic multiferroic magnetoelectric coupling effect. Through incorporating the third component into binary crystals, a dimerization between neighbor donor and acceptor is induced to form a lattice symmetry breaking, where a nonpolar to polar phase transition is ensuing to lead to a dipolar polarization. Magnetic field can effectively tune the dipolar polarization to present a magnetoelectric coupling effect. Moreover, the introduction of the third component can result in a rearrangement in molecular configuration to modify the electron–phonon interaction. As a result, anisotropic magnetism is observed due to anisotropic electron–phonon coupling in ternary crystals. Overall, this study forecasts that incorporating an appropriate third component is a potential method for designing all organic multiferroics.     

Bifurcations in dynamical systems with interior symmetry

We propose a definition of interior symmetry in the context of general dynamical systems. This concept appeared originally in the theory of coupled cell networks, as a generalization of the idea of symmetry of a network. The notion of interior symmetry introduced here can be seen as a special form of forced symmetry breaking of an equivariant system of differential equations. Indeed, we show that a dynamical system with interior symmetry can be written as the sum of an equivariant system and a ‘perturbation term’ which completely breaks the symmetry. Nonetheless, the resulting dynamical system still retains an important feature common to systems with symmetry, namely, the existence of flow-invariant subspaces. We define interior symmetry breaking bifurcations in analogy with the definition of symmetry breaking bifurcation from equivariant bifurcation theory and study the codimension one steady-state and Hopf bifurcations. Our main result is the full analogues of the well-known Equivariant Branching Lemma and the Equivariant Hopf Theorem from the bifurcation theory of equivariant dynamical systems in the context of interior symmetry breaking bifurcations.     

Finite-Wave-Vector Phonon Coupling to Degenerate Electronic States in La2−xSrxCuO4

We consider finite-k electron–phonon coupling appropriate for a superconductor with a very short coherence length and local intersite pairs. From group theoretical analysis we find that k ≠ 0 phonons can couple to degenerate electronic states in La_{2? x} Sr _x CuO₄ and a Jahn-Teller-like distortion is found to be operative for E _g- and E _u-symmetry O states. Experimentally observed anomalies in inelastic neutron scattering, ESR, and EXAFS are found to be consistent with such an interaction of the τ₁ symmetry Σ-point mode with the planar O P _x and P _y states. The proposed interaction is found to naturally facilitate symmetry breaking associated with pairing and/or stripe formation.     

Vortex Precession in a Rotating Nonaxisymmetric Trapped Bose-Einstein Condensate

We study the precession of an off-axis straight vortex in a rotating non-axisymmetric harmonic trap in the Thomas-Fermi (TF) regime. A time-dependent variational Lagrangian analysis yields the dynamical equations of the vortex and the precessional angular velocity in two-dimensional (2D) and three-dimensional (3D) condensates.     

Recapitulating tumour microenvironment in chitosan–gelatin three-dimensional scaffolds: an improved in vitro tumour model

Owing to the reduced co-relationship between conventional flat Petri dish culture (two-dimensional) and the tumour microenvironment, there has been a shift towards three-dimensional culture systems that show an improved analogy to the same. In this work, an extracellular matrix (ECM)-mimicking three-dimensional scaffold based on chitosan and gelatin was fabricated and explored for its potential as a tumour model for lung cancer. It was demonstrated that the chitosan–gelatin (CG) scaffolds supported the formation of tumoroids that were similar to tumours grown in vivo for factors involved in tumour-cell–ECM interaction, invasion and metastasis, and response to anti-cancer drugs. On the other hand, the two-dimensional Petri dish surfaces did not demonstrate gene-expression profiles similar to tumours grown in vivo. Further, the three-dimensional CG scaffolds supported the formation of tumoroids, using other types of cancer cells such as breast, cervix and bone, indicating a possible wider potential for in vitro tumoroid generation. Overall, the results demonstrated that CG scaffolds can be an improved in vitro tool to study cancer progression and drug screening for solid tumours.