Introduction

Luckhurst, G. R.; Sluckin, T. J.

doi:10.1002/9781118696316.ch1

Cited by 13 publications

(15 citation statements)

References 88 publications

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“…We call this the "ordered phase" of the system or "uniaxial", since it possesses one axis of symmetry (following the terminology of liquid crystals; Gramsbergen et al 1986;Luckhurst & Sluckin 2015).…”

Section: One-component Systemsmentioning

confidence: 99%

Isotropic–Nematic Phase Transitions in Gravitational Systems

Roupas

Kocsis

Tremaine

2017

ApJ

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We examine dense self-gravitating stellar systems dominated by a central potential, such as nuclear star clusters hosting a central supermassive black hole. Different dynamical properties of these systems evolve on vastly different timescales. In particular, the orbital-plane orientations are typically driven into internal thermodynamic equilibrium by vector resonant relaxation before the orbital eccentricities or semimajor axes relax. We show that the statistical mechanics of such systems exhibit a striking resemblance to liquid crystals, with analogous ordered-nematic and disordered-isotropic phases. The ordered phase consists of bodies orbiting in a disk in both directions, with the disk thickness depending on temperature, while the disordered phase corresponds to a nearly isotropic distribution of the orbit normals. We show that below a critical value of the total angular momentum, the system undergoes a first-order phase transition between the ordered and disordered phases. At the critical point the phase transition becomes second-order while for higher angular momenta there is a smooth crossover. We also find metastable equilibria containing two identical disks with mutual inclinations between 90• and 180• .

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Section: One-component Systemsmentioning

confidence: 99%

Isotropic–Nematic Phase Transitions in Gravitational Systems

Roupas

Kocsis

Tremaine

2017

ApJ

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“…For instance, the true point-like or ring-like nature of the core has been debated 20 . Recently, this problem has been the object of a renewed interest 17 , 18 , also using molecular level, off-lattice, simulations 21 , like in the work of de Pablo and his group 22 , 23 , but the majority of the studies concerns uniaxial nematics formed of uniaxial particles, notwithstanding the fact that, even if biaxial nematics 24 are still rare, the majority of mesogens is not uniaxial and would be better represented by biaxial objects. Some theoretical speculations regarding nematic droplets formed by biaxial molecules have been put forward 4 , 15 , but computer simulations tackling this problem have been scarce (see, however 25 ).…”

Section: Introductionmentioning

confidence: 99%

On the Defect Structure of Biaxial Nematic Droplets

Chiccoli

Evangelista

Pasini

et al. 2018

Sci Rep

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We present a detailed Monte Carlo study of the effects of molecular biaxiality on the defect created at the centre of a nematic droplet with radial anchoring at the surface. We have studied a lattice model based on a dispersive potential for biaxial mesogens [Luckhurst et al., Mol. Phys. 30, 1345 (1975)] to investigate how increasing the biaxiality influences the molecular organisation inside the confined system. The results are compared with those obtained from a continuum theory approach. We find from both approaches that the defect core size increases by increasing the molecular biaxiality, hinting at a non universal behaviour previously not reported.

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“…As a result, colliding non-Abelian vortices cannot reconnect without leaving traces of the process, but must instead form a connecting rung vortex. Noncommuting defects appear as cosmic strings in theories of the early universe [4], and have been predicted in BN liquid crystals [11].Despite long-standing experimental efforts, BN phases in liquid crystals have experimentally proved more elusive than originally anticipated [12]. In atomic systems, the topological classification and dynamics of non-Abelian vortices have theoretically been studied in the cyclic phase of spin-2 [13-16] and in spin-3 BECs [17], though it remains uncertain whether any alkali-metal atoms exhibit the corresponding ground states.…”

mentioning

confidence: 99%

“…Despite long-standing experimental efforts, BN phases in liquid crystals have experimentally proved more elusive than originally anticipated [12]. In atomic systems, the topological classification and dynamics of non-Abelian vortices have theoretically been studied in the cyclic phase of spin-2 [13-16] and in spin-3 BECs [17], though it remains uncertain whether any alkali-metal atoms exhibit the corresponding ground states.…”

mentioning

confidence: 99%

Core Structure and Non-Abelian Reconnection of Defects in a Biaxial Nematic Spin-2 Bose-Einstein Condensate

Borgh

Ruostekoski

2016

Phys. Rev. Lett.

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We calculate the energetic structure of defect cores and propose controlled methods to imprint a nontrivially entangled vortex pair that undergoes non-Abelian vortex reconnection in a biaxial nematic spin-2 condensate. For a singular vortex, we find three superfluid cores in addition to depletion of the condensate density. These exhibit order parameter symmetries that are different from the discrete symmetry of the biaxial nematic phase, forming an interface between the defect and the bulk superfluid. We provide a detailed analysis of phase mixing in the resulting vortex cores and find an instability dependent upon the orientation of the order parameter. We further show that the spin-2 condensate is a promising system for observing spontaneous deformation of a point defect into an "Alice ring" that has so far avoided experimental detection.Topological defects and textures are ubiquitous across physical systems that seemingly have little in common [1], from liquid crystals [2] and superfluids [3] to cosmic strings [4]. They arise generically from symmetries of a ground state that is described by an order parameter [5]-a function parametrizing the set of physically distinguishable, energetically degenerate states. In the simple example of a scalar superfluid, the order parameter is the phase of the macroscopic wave function. More generally it may be a vector or tensor that is symmetric under particular transformations. In a uniaxial nematic (UN), the order parameter is cylindrically symmetric around a locally defined axis. It also exhibits a twofold discrete symmetry under reversal of the cylinder axis, which leads to half-quantum vortices (HQVs) in atomic spinor BoseEinstein condensates (BECs) [6][7][8][9] and superfluid liquid 3 He [10], and to π disclinations in liquid crystals [1,2]. In a biaxial nematic (BN), also the cylindrical symmetry is broken into the fully discrete symmetry of a rectangular brick, with dramatic consequences: the BN is the simplest order parameter that supports non-Abelian vortices that do not commute [5,11]. As a result, colliding non-Abelian vortices cannot reconnect without leaving traces of the process, but must instead form a connecting rung vortex. Noncommuting defects appear as cosmic strings in theories of the early universe [4], and have been predicted in BN liquid crystals [11].Despite long-standing experimental efforts, BN phases in liquid crystals have experimentally proved more elusive than originally anticipated [12]. In atomic systems, the topological classification and dynamics of non-Abelian vortices have theoretically been studied in the cyclic phase of spin-2 [13-16] and in spin-3 BECs [17], though it remains uncertain whether any alkali-metal atoms exhibit the corresponding ground states. Consequently, any physical system where non-Abelian defects may be reliably studied is still lacking.Spin-2 BECs exhibit-in addition to the ferromagnetic (FM) and cyclic phases-both UN and BN phases [18][19][20], which, however, are degenerate at the mean-field level. Beyond mean-fi...

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Introduction

Cited by 13 publications

References 88 publications

Isotropic–Nematic Phase Transitions in Gravitational Systems

Isotropic–Nematic Phase Transitions in Gravitational Systems

On the Defect Structure of Biaxial Nematic Droplets

Core Structure and Non-Abelian Reconnection of Defects in a Biaxial Nematic Spin-2 Bose-Einstein Condensate

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