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

This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

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The electronic properties of graphene

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

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Many-Body Physics with Ultracold Gases

Resonantly-paired fermionic superfluids

We study D-dimensional polymerized membranes embedded in d dimensions using a self-consistent screening approximation. It is exact for large d to order 1/d, for any d to order \ensuremath{\epsilon}=4-D, and for d=D. For flat physical membranes (D=2, d=3) it predicts a roughness exponent \ensuremath{\zeta}=0.590. For phantom membranes at the crumpling transition the size exponent is \ensuremath{\nu}=0.732. It yields identical lower critical dimension for the flat phase and crumpling transition ${\mathit{D}}_{\mathrm{lc}}$(d)=2d/(d+1) (${\mathit{D}}_{\mathrm{lc}}$= \ensuremath{\surd}2 for codimension 1). For physical membranes with random quenched curvature \ensuremath{\zeta}=0.775 in the new T=0 flat phase in good agremeent with simulations.

Self-consistent theory of polymerized membranes.

We review the physics of pair-density wave (PDW) superconductors. We begin with a macroscopic description that emphasizes order induced by PDW states, such as charge-density wave, and discuss relat...

The Physics of Pair-Density Waves: Cuprate Superconductors and Beyond

We map out the detuning-magnetization phase diagram for a magnetized (unequal number of atoms in two pairing hyperfine states) gas of fermionic atoms interacting via an s-wave Feshbach resonance (FR). The phase diagram is dominated by the coexistence of a magnetized normal gas and a singlet-paired superfluid with the latter exhibiting a BCS-Bose Einstein condensate crossover with reduced FR detuning. On the BCS side of strongly overlapping Cooper pairs, a sliver of finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov magnetized phase intervenes between the phase-separated and normal states. In contrast, for large negative detuning a uniform, polarized superfluid, that is, a coherent mixture of singlet Bose-Einstein-condensed molecules and fully magnetized single-species Fermi sea, is a stable ground state.

BEC-BCS Crossover in ``Magnetized'' Feshbach-Resonantly Paired Superfluids

Motivated by recent studies of fractons, we demonstrate that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid. The topological defects of elasticity theory map onto charges of the tensor gauge theory, with disclinations and dislocations corresponding to fractons and dipoles, respectively. The transverse and longitudinal phonons of crystals map onto the two gapless gauge modes of the gauge theory. The restricted dynamics of fractons matches with constraints on the mobility of lattice defects. The duality leads to numerous predictions for phases and phase transitions of the fracton system, such as the existence of gauge theory counterparts to the (commensurate) crystal, supersolid, hexatic, and isotropic fluid phases of elasticity theory. Extensions of this duality to generalized elasticity theories provide a route to the discovery of new fracton models. As a further consequence, the duality implies that fracton phases are relevant to the study of interacting topological crystalline insulators.

Leo Radzihovsky

Papers

Resonantly-paired fermionic superfluids

Self-consistent theory of polymerized membranes.

The Physics of Pair-Density Waves: Cuprate Superconductors and Beyond

BEC-BCS Crossover in ``Magnetized'' Feshbach-Resonantly Paired Superfluids

Fracton-Elasticity Duality