A physical standard of the unit of electrical resistance based on the quantum Hall effect

Pudalov, V. M.; Semenchinskiǐ, S. G.

doi:10.1070/pu1988v031n09abeh005627

Cited by 8 publications

(2 citation statements)

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“…Classic toy models include the 1D transverse field Ising Model, which is known to have a transition from an unordered to ordered phase at a critical magnetic field strength 1 . Beyond that, materials with exotic phases, such as topological insulators, or the fractional quantum Hall effect are becoming increasingly important to understand as they become more applicable to real-world applications 4 , 5 .…”

Section: Introductionmentioning

confidence: 99%

Uncomputability of phase diagrams

2021

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The phase diagram of a material is of central importance in describing the properties and behaviour of a condensed matter system. In this work, we prove that the task of determining the phase diagram of a many-body Hamiltonian is in general uncomputable, by explicitly constructing a continuous one-parameter family of Hamiltonians H(φ), where $$\varphi \in {\mathbb{R}}$$ φ ∈ R , for which this is the case. The H(φ) are translationally-invariant, with nearest-neighbour couplings on a 2D spin lattice. As well as implying uncomputablity of phase diagrams, our result also proves that undecidability can hold for a set of positive measure of a Hamiltonian’s parameter space, whereas previous results only implied undecidability on a zero measure set. This brings the spectral gap undecidability results a step closer to standard condensed matter problems, where one typically studies phase diagrams of many-body models as a function of one or more continuously varying real parameters, such as magnetic field strength or pressure.

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Section: Introductionmentioning

confidence: 99%

Uncomputability of phase diagrams

2021

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“…In Gaidukov's laboratory this research was performed by young female PhD and graduate students. One of the Gaidukov's PhD student, Elena Goliamina, became my wife, and for this reason I also became indirectly involved in the "whisker business", have read Peschansky's papers, and even have done some research on tiny whisker crystals grown by Gaidukov [4].…”

Section: Introductionmentioning

confidence: 99%

Valentin Peschansky and the puzzles of magnetotransport

Pudalov

2011

Low Temperature Physics

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Starting from the 1950s, the Kharkov school of theoretical physics was one of the world leaders in the theory of metals. In particular, the research by V.G. Peschansky for many years was focused on studying the relationship between magnetic field dependence of resistivity components and the electron energy spectrum. V.G. Peschansky elaborated an elegant theory of magnetoresistance that took into account surface scattering of electrons. The physics of bulk 3D metals was almost exhausted by the end of 1970s and Peschansky extended his research to the low-dimensional electron systems. Through all his scientific life, V.G. Peschansky advocated the idea that magnetoresistance is a powerful tool that can be used to explore rich physics of electron systems. By now, numerous experimental and theoretical studies of magnetoresistance behavior in various systems, from simple to the most complex ones, confirm the fruitfulness of this idea.

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Nucleation of nanoclusters in thermal spikes in solids irradiated with swift heavy ions

Волков

2002

Nuclear Instruments and Methods in Physics Research Section B:

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A physical standard of the unit of electrical resistance based on the quantum Hall effect

Cited by 8 publications

References 1 publication

Uncomputability of phase diagrams

Uncomputability of phase diagrams

Valentin Peschansky and the puzzles of magnetotransport

Nucleation of nanoclusters in thermal spikes in solids irradiated with swift heavy ions

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