By M. Yu. Kagan

This ebook concisely provides the newest developments within the physics of superconductivity and superfluidity and magnetism in novel structures, in addition to the matter of BCS-BEC crossover in ultracold quantum gases and high-Tc superconductors. It additional illuminates the extensive alternate of principles among those heavily similar fields of condensed topic physics during the last 30 years in their dynamic improvement. The content material relies at the author’s unique findings got on the Kapitza Institute, in addition to complicated lecture classes he held on the Moscow Engineering actual Institute, Amsterdam collage, Loughborough college and LPTMS Orsay among 1994 and 2011. as well as the findings of his workforce, the writer discusses the newest options in those fields, received either in Russia and within the West. The booklet involves sixteen chapters that are divided into 4 components. the 1st half describes contemporary advancements in superfluid hydrodynamics of quantum fluids and solids, together with the trendy topic of attainable supersolidity in quantum crystals of 4He, whereas the second one describes BCS-BEC crossover in quantum Fermi-Bose gases and combinations, in addition to within the underdoped states of cuprates. The 3rd half is dedicated to non-phonon mechanisms of superconductivity in unconventional (anomalous) superconductors, together with a few vital features of the speculation of high-Tc superconductivity. |The final half considers the anomalous common country of novel superconductive fabrics and fabrics with immense magnetoresistance (CMR). The publication bargains a invaluable advisor for senior-level undergraduate scholars and graduate scholars, postdoctoral and different researchers focusing on solid-state and low-temperature physics.

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6 Collective Modes of the Lattice. Tkachenko Waves and Kelvin Waves. Melting of the Vortex Lattice According to Sonin in the general case of compressive rotating superfluid with a triangular vortex lattice the spectrum of collective excitations in the long wavelength limit reads (see [39, 40]): ﬄ 4 À Á x2 À c2I kz2 c2t k? 2 2 2 x ¼ 2X þ kkz 2X 2 þ kkz þ ; ð1:2:66Þ 2X x À c2I k2 ls X ¼ "h8m is Tkachenko sound velocity squared, c2I is first sound velocity where c2t ¼ 2q s h " ln db and kz and k\ are the projections of the wave-vector ~ k ðk2 ¼ squared, k ¼ 2m 2 k?

E. the derivative o~ vL ð~ r; tÞ. To ot via ~ establish this connection we express the physically infinitely small differential of the coordinates d~ r (which is large compared with the lattice period, but small compared with the distance over which the vortex configuration varies) in the form (see [31] for more details): d~ r ¼~ ea dN a : ð1:2:12Þ The quantities dNa for two lattice points separated by a distance d~ r are the two projections of d~ r measured in units of the corresponding lattice periods.

For finite temperatures we have classical melting while for T = 0 we can still have quantum melting. 2 Hydrodynamics of Rotating Superfluids 39 and for the search of supersolidity inQuantum crystals (see Chap. 2). The quantum melting for the 2D lattice requires ~ u2 b2 ! 0:07 (see Cooper et al. [53–55]). Note that according to Baym at zero temperature the mean displacement squared for purely 2D flows (kz : 0) reads: 2 1=2 1=2 ~ u nv mc2I 1 mc2I $ $ ; ð1:2:76Þ p X b2 ns L X 2 1=2 mc where nS is a superfluid particle density.