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.

/pdf/the-electronic-properties-of-graphene-2siyzsnf5w.pdf

The electronic properties of graphene

A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar dynamical phase factor. An explicit general formula for γ(C) is derived in terms of the spectrum and eigenstates of Ĥ(R) over a surface spanning C. If C lies near a degeneracy of Ĥ, γ(C) takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy. As an illustration γ(C) is calculated for spinning particles in slowly-changing magnetic fields; although the sign reversal of spinors on rotation is a special case, the effect is predicted to occur for bosons as well as fermions, and a method for observing it is proposed. It is shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor.

Quantal phase factors accompanying adiabatic changes

Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues.

Quantum Cryptography

Conventional optical components rely on gradual phase shifts accumulated during light propagation to shape light beams. New degrees of freedom are attained by introducing abrupt phase changes over the scale of the wavelength. A two-dimensional array of optical resonators with spatially varying phase response and subwavelength separation can imprint such phase discontinuities on propagating light as it traverses the interface between two media. Anomalous reflection and refraction phenomena are observed in this regime in optically thin arrays of metallic antennas on silicon with a linear phase variation along the interface, which are in excellent agreement with generalized laws derived from Fermat’s principle. Phase discontinuities provide great flexibility in the design of light beams, as illustrated by the generation of optical vortices through use of planar designer metallic interfaces.

http://www.zenogaburro.it/papers/LightPropagation.pdf

Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction

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.

/pdf/many-body-physics-with-ultracold-gases-552s10zfdn.pdf

Many-Body Physics with Ultracold Gases

Although band-limited by the wavelength, optical fields can oscillate arbitrarily fast where the field is weak. Such sub-wavelength detail typically occupies one-third of the area of images, including optical vortices where the local wavenumber diverges.

http://ieeexplore.ieee.org/iel5/5164156/5191447/05191664.pdf

Optical superoscillations

Wave Geometry: a Plurality of Singularities

/pdf/in-support-of-catastrophe-theory-frzrm8kem0.pdf

In support of catastrophe theory

Purpose: To analyze the safety and efficacy of corneal photovitrification (CPV) for improved visions of age-related macular degeneration (AMD) eyes. 
Study Design: Using CPV for improved visions of AMD eyes. 
Place and Duration of Study: New Taipei City, Taiwan, and Austin, TX, USA; between 
April, 2022 and June, 2022. 
Methodology: The CPV efficacy is calculated based on the rate equation given by dM/dt=-k(t) M(t), where M(t) is the PCV-treated corneal stroma; and k(t) is the rate coefficient given by an Arrhenius formula, k(t) = A0 exp[−Ea/(RT(t,z)], where t and z are the laser irradiation time and depth of the cornea stroma; Ea  is the activation energy and R is the gas constant. The temperature spatial and temporal profiles are given by the numerical solutions of a heat diffusion equation with a volume heating source. Various effective depths including the tissue damage depth, temperature penetration depth and conversion depth, governed by the tissue absorption coefficient, light intensity and dose (or irradiation time), and the related threshold values, are introduced in replacing the conventional penetration depth based on a Beer's law. 
Results: The suggested protocol for CPV treatments include: a diode laser at about 2 µm wavelength (with absorption coefficient about 100 cm-1). The laser dose is about 25 J/cm2/spot and irradiation time of 150 ms. 
Conclusion: The efficacy of CPV may be predicted/calculated by our modeling based on rate equation and the corneal stroma temperature rise due to laser heating. The preferred retinal locus (PRL) movement observed post-CPV is caused mainly by neuroadaptation.

Efficacy Analysis of Corneal Photo-vitrification (CPV) for Improved Vision of Age-related Macular Degeneration (AMD) Eyes

A brief review is given of what has been achieved in understanding the discrete spectra of classically chaotic bound quantum systems, emphasising the central role of semiclassical techniques and the unsolved problems associated with the clash between the long-time limit and the semiclassical limit.

Michael V Berry

Papers

Optical superoscillations

Wave Geometry: a Plurality of Singularities

In support of catastrophe theory

Efficacy Analysis of Corneal Photo-vitrification (CPV) for Improved Vision of Age-related Macular Degeneration (AMD) Eyes

Quantum chaology: our knowledge and ignorance