Random-matrix theories in quantum physics : common concepts

We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new "statistical mechanics": Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.

Random Matrix Theories in Quantum Physics: Common Concepts

The transport properties of disordered solids have been the subject of much work since at least the 1950s, but with a new burst of activity during the 1980s which has survived up to the present day. There have been numerous reviews of a more or less specialized nature. The present review aims to fill the niche for a non-specialized review of this very active area of research. The basic concepts behind the theory are introduced with more detailed sections covering experimental results, one-dimensional localization, scaling theory, weak localization, magnetic field effects and fluctuations.

https://iopscience.iop.org/article/10.1088/0034-4885/56/12/001/pdf

Localization: theory and experiment

Nanopore analysis is an emerging technique that involves using a voltage to drive molecules through a nanoscale pore in a membrane between two electrolytes, and monitoring how the ionic current through the nanopore changes as single molecules pass through it. This approach allows charged polymers (including single-stranded DNA, double-stranded DNA and RNA) to be analysed with subnanometre resolution and without the need for labels or amplification. Recent advances suggest that nanopore-based sensors could be competitive with other third-generation DNA sequencing technologies, and may be able to rapidly and reliably sequence the human genome for under $1,000. In this article we review the use of nanopore technology in DNA sequencing, genetics and medical diagnostics.

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Nanopore sensors for nucleic acid analysis

The development of wave optics for light brought many new insights into our understanding of physics, driven by fundamental experiments like the ones by Young, Fizeau, Michelson-Morley and others. Quantum mechanics, and especially the de Broglie’s postulate relating the momentum p of a particle to the wave vector k of an matter wave: k = 2 λ = p/ℏ, suggested that wave optical experiments should be also possible with massive particles (see table 1), and over the last 40 years electron and neutron interferometers have demonstrated many fundamental aspects of quantum mechanics [1].

/pdf/optics-and-interferometry-with-atoms-and-molecules-1vnuwajb51.pdf

Optics and interferometry with atoms and molecules

We report a new method to fabricate electrode-embedded multiple nanopore structures with sub-10 nm diameter, which is designed for electrofluidic applications such as ionic field effect transistors Our method involves patterning pore structures on membranes using e-beam lithography and shrinking the pore diameter by a self-limiting atomic layer deposition process We demonstrate that 70∼80 nm diameter pores can be shrunk down to sub-10 nm diameter and that the ionic transport of KCl electrolyte can be efficiently manipulated by the embedded electrode within the membrane

Ionic field effect transistors with sub-10 nm multiple nanopores.

We characterize inductors fabricated from ultra-thin, approximately 100 nm wide strips of niobium (Nb) and niobium nitride (NbN). These nanowires have a large kinetic inductance in the superconducting state. The kinetic inductance scales linearly with the nanowire length, with a typical value of 1 nH/um for NbN and 44 pH/um for Nb at a temperature of 2.5 K. We measure the temperature and current dependence of the kinetic inductance and compare our results to theoretical predictions. We also simulate the self-resonant frequencies of these nanowires in a compact meander geometry. These nanowire inductive elements have applications in a variety of microwave frequency superconducting circuits.

Tunable superconducting nanoinductors

The authors, demonstrated that 4.5-nm-half-pitch structures could be achieved using electron-beam lithography, followed by salty development. They also hypothesized a development mechanism for hydrogen silsesquioxane, wherein screening of the resist surface charge is crucial in achieving a high initial development rate, which might be a more accurate assessment of developer performance than developer contrast. Finally, they showed that with a high-development-rate process, a short duration development of 15s was sufficient to resolve high-resolution structures in 15-nm-thick resist, while a longer development degraded the quality of the structures with no improvement in the resolution.

http://dspace.mit.edu/bitstream/handle/1721.1/73050/Berggren-Understanding%20of%20hydrogen.pdf?sequence=1

Understanding of hydrogen silsesquioxane electron resist for sub-5-nm-half-pitch lithography

We characterize inductors fabricated from ultra-thin, approximately 100 nm wide strips of niobium (Nb) and niobium nitride (NbN). These nanowires have a large kinetic inductance in the superconducting state. The kinetic inductance scales linearly with the nanowire length, with a typical value of 1 nH µm − 1 for NbN and 44 pH µm − 1 for Nb at a temperature of 2.5 K. We measure the temperature and current dependence of the kinetic inductance and compare our results to theoretical predictions. We also simulate the self-resonant frequencies of these nanowires in a compact meander geometry. These nanowire inductive elements have applications in a variety of microwave frequency superconducting circuits.

https://iopscience.iop.org/article/10.1088/0957-4484/21/44/445202/pdf

We report resistance oscillations as a function of magnetic field for individual aluminum and silver thin-film rings, 1-2 \ensuremath{\mu}m in diameter, between 1.2 and 10 K. This is the first observation in single rings of oscillations with a flux period of $\frac{h}{2e}$ predicted by Al'tshuler et al. Oscillations periodic in $\frac{h}{e}$ are also seen in the 1-\ensuremath{\mu}m Ag rings at higher fields. These electron interference effects in metal rings are the solid-state analog of the Aharonov-Bohm effect for electrons in vacuum.

Michael J. Rooks

Papers

Ionic field effect transistors with sub-10 nm multiple nanopores.

Tunable superconducting nanoinductors

Understanding of hydrogen silsesquioxane electron resist for sub-5-nm-half-pitch lithography

Tunable superconducting nanoinductors

Observation of Aharonov-Bohm electron interference effects with periods h/e and h/2e in individual micron-size, normal-metal rings.