By Boris V. Svistunov, Egor S. Babaev, Nikolay V. Prokof'ev

Covers the cutting-edge in Superfluidity and Superconductivity

Superfluid States of Matter addresses the phenomenon of superfluidity/superconductivity via an emergent, topologically secure consistent of movement and covers issues built over the last two decades. The procedure is predicated at the suggestion of isolating common classical-field superfluid homes of topic from the underlying system’s “quanta.” The textual content starts off via deriving the final actual ideas at the back of superfluidity/superconductivity in the classical-field framework and gives a deep knowing of all key elements when it comes to the dynamics and statistics of a classical-field system.

It proceeds by means of explaining how this framework emerges in sensible quantum platforms, with examples that come with liquid helium, high-temperature superconductors, ultra-cold atomic bosons and fermions, and nuclear subject. The ebook additionally bargains numerous robust sleek methods to the topic, reminiscent of practical and direction integrals.

Comprised of 15 chapters, this text:

  • Establishes the elemental macroscopic homes of superfluids and superconductors in the paradigm of the classical subject field
  • Deals with a single-component impartial topic field
  • Considers basics and homes of superconductors
  • Describes new physics of superfluidity and superconductivity that arises in multicomponent systems
  • Presents the quantum-field point of view at the stipulations below which classical-field description is suitable in bosonic and fermionic systems
  • Introduces the trail critical formalism
  • Shows how Feynman course integrals could be successfully simulated with the trojan horse algorithm
  • Explains why nonsuperfluid (insulating) flooring states of standard and disordered bosons take place lower than acceptable conditions
  • Explores superfluid solids (supersolids)
  • Discusses the wealthy dynamics of vortices and diverse points of superfluid turbulence at T →0
  • Provides account of BCS thought for the weakly interacting Fermi gas
  • Highlights and analyzes the main an important advancements that has ended in the present figuring out of superfluidity and superconductivity
  • Reviews the range of superfluid and superconducting platforms to be had this present day in nature and the laboratory, in addition to the states that experimental attention is at the moment actively pursuing

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95) In various subfields of physics, this equation is known under the generic name of nonlinear Schr¨odinger equation (NLSE). In the theory of quantum gases—closest to the subject of this book—this equation is called the time-dependent Gross–Pitaevskii equation (GPE), with the reservation that GPE is traditionally associated with the Bose-Einstein condensate (BEC), and thus superfluidity. 95) do feature superfluidity, there is a normal-fluid regime as well. 11) is conserved by GPE. For a given N , there is a ground state, ψ0 , corresponding to the minimal possible energy.

R0 →ri . 122). ∗ That is, the freedom of replacing a → a + ∇f , where f is an arbitrary smooth scalar field; for ∇·a 0, choose f such that Δf = −∇ · a. 119) is∗ Evort = w(r1 ) · w(r2 ) 3 d r1 d 3 r2 . 119). 72)], associated with the flow pattern. 130). This brings us to Mi Pvort = πn0 ri × dli . 72). In two dimensions, an extra simplification arises due to the analogy with 2D electrostatics. 121), the Laplace equation Δu = 0, everywhere except for the vortex centers, at which u is singular and zˆ is a unit 3D vector perpendicular to the xy-plane in which the vector r lives.

By the same argument, vortices in 3D are lines with no free ends in the bulk: They either form closed loops or terminate at the box boundaries. Vortex defects in 3D are often referred to as vortex lines or filaments. In 2D, elementary vortex defects have point singularities. 113) where ϕ is the azimuthal angle and ρ is the distance from the vortex line. The solution is not diverging at ρ = 0, implying n(ρ) ∝ ρ2 at ρ → 0. 114) By dimensional argument, it is clear that the size of the core—the region where the density n is significantly different from its asymptotic uniform value n0 —is on the order of the healing length l0 .

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