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Toshiyuki Fujii

Publications and source records attributed to Toshiyuki Fujii.

12 recordsLinked to original sources
arXiv2026

Landau Theory for Commensurate Charge-Density Waves Coupled to Uniform Lattice Deformation

We formulate a minimal Landau theory for a charge-density wave (CDW) whose commensurability is defined with respect to a deformed lattice. The motivation is provided by recent observations on an isolated single NbS$_3$ chain, which exhibits a commensurate CDW state accompanied by a $6\%$ shrinkage of the lattice constant. A uniform stretch $a_0\to a_0(1+\varepsilon)$ changes the reciprocal lattice wave number to $G(\varepsilon)=G_0/(1+\varepsilon)$, so that an $N$-fold commensurate CDW has the wave number $Q_\mathrm{C}(\varepsilon)=G(\varepsilon)/N$, whereas the wave number $Q_\mathrm{IC}$ favored by the incommensurate instability remains fixed. We propose an amplitude-strain free energy for both $N=3$ and $N=4$, in which the CDW induces a finite uniform strain by relieving the mismatch between $Q_\mathrm{C}(\varepsilon)$ and $Q_\mathrm{IC}$. The mismatch is shared between the CDW and the lattice in a proportion set by their stiffness ratio; since the CDW stiffness grows with the CDW amplitude, the lattice takes up an increasing share of the mismatch as the CDW develops. Our results suggest a reexamination of lock-in theories and of strain-tuning experiments on density-wave systems.

cond-mat.other↗
arXiv2025

Representations of Josephson junction on the unit circle and the derivations of Mathieu operators and Fraunhofer patterns

The Hamiltonian J of the Josephson junction is introduced as a self-adjoint operator on l2 tensor l2. It is shown that J can also be realized as a self-adjoint operator HS1 on L2(S1) tensor L2(S1), from which a Mathieu operator given by "-d^2/dθ^2 - 2α cos θ" is derived. A fiber decomposition of HS1 with respect to the total particle number is established, and the action on each fiber is analyzed. In the presence of a magnetic field, a phase shift defines the magnetic Josephson junction Hamiltonian HS1(Φ) and the Josephson current IS1(Φ). For a constant magnetic field inducing a local phase shift Φ(x), the corresponding local current IS1(Φ(x)) is computed, and it is proved that the Fraunhofer pattern arises naturally.

math-ph↗
arXiv2023

Analogue black-white hole solitons in travelling wave parametric amplifiers with superconducting nonlinear asymmetric inductive elements

We show that existing travelling wave parametric amplifier (TWPA) setups, using superconducting nonlinear asymmetric inductive elements (SNAILs), admit soliton solutions that act as analogue event horizons. The SNAIL-TWPA circuit dynamics are described by the Korteweg-de Vries (KdV) or modified Korteweg-de Vries (mKdV) equations in the continuum field approximation, depending on the external magnetic flux bias, and validated numerically. The soliton spatially modulates the velocity for weak probes, resulting in the effective realization of analogue black hole and white hole event horizon pairs. The SNAIL external magnetic flux bias tunability facilitates a three-wave mixing process, which enhances the prospects for observing Hawking photon radiation.

quant-ph↗
arXiv2020

The Nakano-Nishijima-Gell-Mann Formula From Discrete Galois Fields

The well known Nakano-Nishijima-Gell-Mann (NNG) formula relates certain quantum numbers of elementary particles to their charge number. This equation, which phenomenologically introduces the quantum numbers $I_z$ (isospin), $S$ (strangeness), etc., is constructed using group theory with real numbers $\mathbb{R}$. But, using a discrete Galois field $\mathbb{F}_p$ instead of $\mathbb{R}$ and assuring the fundamental invariance laws such as unitarity, Lorentz invariance, and gauge invariance, we derive the NNG formula deductively from Meson (two quarks) and Baryon (three quarks) representations in a unified way. Moreover, we show that quark confinement ascribes to the inevitable fractionality caused by coprimeness between half-integer (1/2) of isospin and number of composite particles (e.g. three).

hep-ph↗
arXiv2020

Theoretical Studies on Quantum Walks with a Time-varying Coin

Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically time-varying coin both numerically and analytically, in order to explore the controllability of quantum walks while preserving its random nature.

quant-ph↗
arXiv2017

Incommensurate Charge Density Wave as Quantum Space-Time Crystal

A quantum time crystal (QTC) is a novel quantum mechanical ground state that was recently proposed by Wilczek. Although many QTC models have been proposed, it is not clear yet if such states are possible. We propose the idea that an incommensurate charge density wave (ICDW) forms a quantum space crystal (QSC), which is an extension of a QTC in the spatial domain. Consequently, a rotating ring-shaped ICDW naturally forms a quantum space-time crystal (QSTC), which combines the two concepts of QTC and QSC. The breaking of space-time translation symmetry is understood using time-dependent density matrices. Furthermore, we show that this model can be observed in real systems such as TaS$_3$ ring crystals at finite temperature. Our results suggest that QTC/QSTC can exist.

quant-ph↗
arXiv2017

Quantum Time Crystal By Decoherence: Proposal With Incommensurate Charge Density Wave Ring

We show that time translation symmetry of a ring system with a macroscopic quantum ground state is broken by decoherence. In particular, we consider a ring-shaped incommensurate charge density wave (ICDW ring) threaded by a fluctuating magnetic flux: the Caldeira-Leggett model is used to model the fluctuating flux as a bath of harmonic oscillators. We show that the charge density expectation value of a quantized ICDW ring coupled to its environment oscillates periodically. The Hamiltonians considered in this model are time independent unlike "Floquet time crystals" considered recently. Our model forms a metastable quantum time crystal with a finite length in space and in time.

quant-ph↗
arXiv2009

Proposal for testing Einstein's moon using three-time correlations

Quantum mechanics has predicted many counterintuitive phenomena in daily life, and has changed our view of the world. Among such predictions, the existence of a macroscopic object in superposition is especially unbelievable. As Einstein asked, "Do you really believe that the moon exists only when you look at it?". However, recent experimental results on a mesoscopic scale will ultimately require us to dismiss commonsense so-called macroscopic reality. Leggett and Garg applied the Bell scheme for testing local realism to the time evolution of a macroscopic two-state system, and proposed a temporal version of the Bell inequality (the Leggett-Garg (LG) inequality) for testing macroscopic realism. However, as with the Bell inequality, the statistical approach behind this scheme may be less effective in showing clear incompatibility. Here we propose a temporal version of the Greenberger-Horne-Zeilinger (GHZ) scheme without statistical treatment for testing Einstein's moon using three-time correlations.

cond-mat.mes-hall↗
arXiv2009

Quantum Knitting Computer

We propose a fluxon-controlled quantum computer incorporated with three-qubit quantum error correction using special gate operations, i.e., joint-phase and SWAP gate operations, inherent in capacitively coupled superconducting flux qubits. The proposed quantum computer acts exactly like a knitting machine at home.

quant-ph↗
arXiv2009

Fluxon-based generation of graph states in Josephson qubits

Graph states are a special kind of multiparticle entangled state with great potential for applications in quantum information technologies, especially in measurement-based quantum computers. These states cause significant reductions of the number of qubits needed for a given computation, leading to shorter execution time. Here we propose a simple scheme for generating such graph states by using special gate operations, i.e., control-phase and swap gate operations, inherent in superconducting quantum nanocircuits.

cond-mat.supr-con↗
arXiv2007

Time dilation of a bound half-fluxon pair in a long Josephson junction with a ferromagnetic insulator

The fluxon dynamics in a long Josephson junction with a ferromagnetic insulating layer is investigated. It is found that the Josephson phase obeys a double sine-Gordon equation involving a bound pi fluxon solution, and the internal oscillations of the bound pair acting as a clock exhibit Lorentz reductions in their frequencies regarded as a relativistic effect in the time domain, i.e., time dilation. This is the complement to the Lorentz contraction of fluxons with no clock. A possible observation scheme is also discussed.

cond-mat.supr-con↗