There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.

https://arxiv.org/pdf/cond-mat/9806038.pdf

Theory of Bose-Einstein condensation in trapped gases

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

The 1937 theoretical discovery of Majorana fermions-whose defining property is that they are their own anti-particles-has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review paper highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic 'topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to 'engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions-the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.

/pdf/new-directions-in-the-pursuit-of-majorana-fermions-in-solid-5cpnozn547.pdf

New directions in the pursuit of Majorana fermions in solid state systems.

We describe the nature of charge transport at non-zero temperatures (T ) above the two-dimensional (d) superuid-insulator quantum critical point. We argue that the transport is characterized by inelastic collisions among thermally excited carriers at a rate of order kBT=h. This implies that the transport at frequencies ! kBT=h is in the hydrodynamic, collision-dominated (or ‘incoherent’) regime, while ! kBT=h is the collisionless (or ‘phasecoherent’) regime. The conductivity is argued to be e 2 =h times a non-trivial universal scaling function ofh!=kBT , and not independent of h!=kBT ,a s has been previously claimed, or implicitly assumed. The experimentally measured d.c. conductivity is the hydrodynamic h!=kBT ! 0 limit of this function, and is a universal number times e 2 =h, even though the transport is incoherent. Previous work determined the conductivity by incorrectly assuming it was also equal to the collisionless h!=kBT !1limit of the scaling function, which actually describes phase-coherent transport with a conductivity given by a dierent universal number times e 2 =h. We provide the rst computation of the universal d.c. conductivity in a disorder-free boson model, along with explicit crossover functions, using a quantum Boltzmann equation and an expansion in =3 d. The case of spin transport near quantum critical points in antiferromagnets is also discussed. Similar ideas should apply to the transitions in quantum Hall systems and to metal-insulator transitions. We suggest experimental tests of our picture and speculate on a new route to self-duality at two-dimensional quantum critical points.

/pdf/nonzero-temperature-transport-near-quantum-critical-points-71ceqt3n46.pdf

Nonzero-temperature transport near quantum critical points

We introduce a strong-disorder renormalization group (RG) approach suitable for investigating the quasiparticle excitations of disordered superconductors in which the quasiparticle spin is not conserved. We analyze one-dimensional models with this RG and with elementary transfer matrix methods. We find that such models with broken spin rotation invariance generically lie in one of two topologically distinct localized phases. Close enough to the critical point separating the two phases, the system has a power-law divergent low-energy density of states (with a nonuniversal continuously varying power law) in either phase, due to quantum Griffiths singularities. This critical point belongs to the same infinite-disorder universality class as the one-dimensional particle-hole symmetric Anderson localization problem, while the Griffiths phases in the vicinity of the transition are controlled by lines of strong (but not infinite) disorder fixed points terminating in the critical point.

/pdf/griffiths-effects-and-quantum-critical-points-in-dirty-2mz6nxw63e.pdf

Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples

We study hard-core bosons with unfrustrated hopping ($t$) and nearest neighbor repulsion ($U$) (spin $S=1/2$ $XXZ$ model) on the triangular lattice. At half filling, the system undergoes a zero temperature ($T$) quantum phase transition from a superfluid phase at small $U$ to a supersolid at ${U}_{c}\ensuremath{\approx}4.45$ in units of $2t$. This supersolid phase breaks the lattice translation symmetry in a characteristic $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ pattern, and is remarkably stable\char22{}indeed, a smooth extrapolation of our results indicates that the supersolid phase persists for arbitrarily large $U/t$.

https://arxiv.org/pdf/cond-mat/0505257.pdf

Persistent supersolid phase of hard-core bosons on the triangular lattice.

We study the physics of hard-core bosons with unfrustrated hopping (t) and nearest-neighbor repulsion (V) on the three dimensional pyrochlore lattice. At half-filling, we demonstrate that the small V/t superfluid state eventually becomes unstable at large enough V/t to an unusual insulating state which displays no broken lattice translation symmetry. Equal time and static density correlators in this insulator are well described by a mapping to electric field correlators in the Coulomb phase of a U(1) lattice gauge theory, allowing us to identify this insulator with a U(1) fractionalized Mott-insulating state. The possibility of observing this phase in suitably designed atom-trap experiments with ultracold atoms is also discussed, as are specific experimental signatures.

https://arxiv.org/pdf/cond-mat/0702029.pdf

Unusual liquid state of hard-core bosons on the pyrochlore lattice.

We discuss the theory of the nonzero temperature $(T)$ spin dynamics and transport in one-dimensional Heisenberg antiferromagnets with a gap $\ensuremath{\Delta}$. For $T\ensuremath{\ll}\ensuremath{\Delta}$, we develop a semiclassical picture of thermally excited particles. Multiple inelastic collisions between the particles are crucial, and are described by a two-particle $\mathcal{S}$ matrix which is shown to have a superuniversal form at low momenta. This is established by computations on the $O(3)$ $\ensuremath{\sigma}$ model, and strong- and weak-coupling expansions (the latter using a Majorana fermion representation) for the two-leg $S=1/2$ Heisenberg antiferromagnetic ladder. As an aside, we note that the strong-coupling calculation reveals an $S=1$, two-particle bound state which leads to the presence of a second peak in the $T=0$ inelastic neutron-scattering (INS) cross section for a range of values of momentum transfer. We obtain exact, or numerically exact, universal expressions for the thermal broadening of the quasiparticle peak in the INS cross section, the spin diffusivity, and for the field dependence of the NMR relaxation rate ${1/T}_{1}$ of the effective semiclassical model; these are expected to be asymptotically exact for the quantum antiferromagnets in the limit $T\ensuremath{\ll}\ensuremath{\Delta}$. The results for ${1/T}_{1}$ are compared with the experimental findings of Takigawa et al. [Phys. Rev. Lett. 76, 2173 (1996)] and the agreement is quite good. In the regime $\ensuremath{\Delta}lTl$(a typical microscopic exchange) and we argue that a complementary description in terms of semiclassical waves applies, and give some exact results for the thermodynamics and dynamics.

/pdf/spin-dynamics-and-transport-in-gapped-one-dimensional-dwwuc826t8.pdf

Kedar Damle

Papers

Nonzero-temperature transport near quantum critical points

Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples

Persistent supersolid phase of hard-core bosons on the triangular lattice.

Unusual liquid state of hard-core bosons on the pyrochlore lattice.

Spin dynamics and transport in gapped one-dimensional Heisenberg antiferromagnets at nonzero temperatures