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

Physical Review B

In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature\(\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K\) where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.

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Particle Creation by Black Holes

Associate DIETRICH BELITZ, University of Oregon Editors: Condensed Matter Physics (Theoretical) J. IGNACIO CIRAC, Max-Planck-Institut für Quantenoptik Quantum Information RAYMOND E. GOLDSTEIN, University of Cambridge Biological Physics ARTHUR F. HEBARD, University of Florida Condensed Matter Physics (Experimental) RANDALL D. KAMIEN, University of Pennsylvania Soft Condensed Matter DANIEL KLEPPNER, Massachusetts Institute of Technology Atomic, Molecular, and Optical Physics (Experimental) PAUL G. LANGACKER, Institute for Advanced Study, Princeton University Particle Physics (Theoretical) VERA LÜTH, Stanford University Particle Physics (Experimental) DAVID D. MEYERHOFER, University of Rochester Physics of Plasmas and Matter at High-Energy Density WITOLD NAZAREWICZ, University of Tennessee, Oak Ridge National Laboratory Nuclear Physics JOHN H. SCHWARZ, California Institute of Technology Mathematical Physics FRIEDRICH-KARL THIELEMANN, Universität Basel Astrophysics Senior Assistant Editor: DEBBIE BRODBAR, APS Editorial Office American Physical Society

Reviews of Modern Physics

A review is given on the foundations and applications of non-Hermitian classical and quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra, including Jordan normal form, biorthogonality, exceptional points, pseudo-Hermiticity and parity-time symmetry, are delineated in a pedagogical and mathematically coherent manner. Building on these, we provide an overview of how diverse classical systems, ranging from photonics, mechanics, electrical circuits, acoustics to active matter, can be used to simulate non-Hermitian wave physics. In particular, we discuss rich and unique phenomena found therein, such as unidirectional invisibility, enhanced sensitivity, topological energy transfer, coherent perfect absorption, single-mode lasing, and robust biological transport. We then explain in detail how non-Hermitian operators emerge as an effective description of open quantum systems on the basis of the Feshbach projection approach and the quantum trajectory approach. We discuss their applications to physical systems relevant to a variety of fields, including atomic, molecular and optical physics, mesoscopic physics, and nuclear physics with emphasis on prominent phenomena/subjects in quantum regimes, such as quantum resonances, superradiance, continuous quantum Zeno effect, quantum critical phenomena, Dirac spectra in quantum chromodynamics, and nonunitary conformal field theories. Finally, we introduce the notion of band topology in complex spectra of non-Hermitian systems and present their classifications by providing the proof, firstly given by this review in a complete manner, as well as a number of instructive examples. Other topics related to non-Hermitian physics, including nonreciprocal transport, speed limits, nonunitary quantum walk, are also reviewed.

Non-Hermitian Physics

We investigate the transport properties of neutral, fermionic atoms passing through a one-dimensional quantum wire containing a mesoscopic lattice. The lattice is realized by projecting individually controlled, thin optical barriers on top of a ballistic conductor. Building an increasingly longer lattice, one site after another, we observe and characterize the emergence of a band insulating phase, demonstrating control over quantum-coherent transport. We explore the influence of atom-atom interactions and show that the insulating state persists as contact interactions are tuned from moderately to strongly attractive. Using bosonization and classical Monte Carlo simulations, we analyze such a model of interacting fermions and find good qualitative agreement with the data. The robustness of the insulating state supports the existence of a Luther-Emery liquid in the one-dimensional wire. Our work realizes a tunable, site-controlled lattice Fermi gas strongly coupled to reservoirs, which is an ideal test bed for nonequilibrium many-body physics.

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Band and Correlated Insulators of Cold Fermions in a Mesoscopic Lattice

We experimentally study the dynamics of a degenerate one-dimensional Bose gas that is subject to a continuous outcoupling of atoms. Although standard evaporative cooling is rendered ineffective by the absence of thermalizing collisions in this system, we observe substantial cooling. This cooling proceeds through homogeneous particle dissipation and many-body dephasing, enabling the preparation of otherwise unexpectedly low temperatures. Our observations establish a scaling relation between temperature and particle number, and provide insights into equilibration in the quantum world.

Cooling of a One-Dimensional Bose Gas

Nonlinear optical phenomena are typically local. Here, we predict the possibility of highly nonlocal optical nonlinearities for light propagating in atomic media trapped near a nano-waveguide, where long-range interactions between the atoms can be tailored. When the atoms are in an electromagnetically induced transparency configuration, the atomic interactions are translated to long-range interactions between photons and thus to highly nonlocal optical nonlinearities. We derive and analyze the governing nonlinear propagation equation, finding a roton-like excitation spectrum for light and the emergence of order in its output intensity. These predictions open the door to studies of unexplored wave dynamics and many-body physics with highly nonlocal interactions of optical fields in one dimension.

Highly nonlocal optical nonlinearities in atoms trapped near a waveguide

We present measurements of the dynamical structure factor S(q,ω) of an interacting one-dimensional Fermi gas for small excitation energies. We use the two lowest hyperfine levels of the ^{6}Li atom to form a pseudospin-1/2 system whose s-wave interactions are tunable via a Feshbach resonance. The atoms are confined to one dimension by a two-dimensional optical lattice. Bragg spectroscopy is used to measure a response of the gas to density ("charge") mode excitations at a momentum q and frequency ω, as a function of the interaction strength. The spectrum is obtained by varying ω, while the angle between two laser beams determines q, which is fixed to be less than the Fermi momentum k_{F}. The measurements agree well with Tomonaga-Luttinger theory.

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Measurement of the Dynamical Structure Factor of a 1D Interacting Fermi Gas.

We present numerical results demonstrating the possibility of thermalization of single-particle observables in a one-dimensional system, which is integrable in both the quantum and classical (mean-field) descriptions (a quasicondensate of ultracold, weakly interacting bosonic atoms are studied as a definite example). We find that certain initial conditions admit the relaxation of single-particle observables to the equilibrium state reasonably close to that corresponding to the Bose-Einstein thermal distribution of Bogoliubov quasiparticles.

Pjotrs Grišins

Papers

Band and Correlated Insulators of Cold Fermions in a Mesoscopic Lattice

Cooling of a One-Dimensional Bose Gas

Highly nonlocal optical nonlinearities in atoms trapped near a waveguide

Measurement of the Dynamical Structure Factor of a 1D Interacting Fermi Gas.

Thermalization in a one-dimensional integrable system