Quantum anomaly, a situation in which the symmetry of the classical action fails to be a symmetry of the full quantum theory, is a topic of great interest in quantum field theory. This is because it plays various important roles in physics and has beautiful mathematical structures.

In a new study, researchers from Japan explored perturbative anomalies in a system of N Dirac fermions with spacetime dependent mass (or the Higgs field that couples with the fermions through the Yukawa coupling) that included external gauge fields associated with *U(N) _{+ }x U(N)_{-} *chiral symmetry for even dimensions and

Interestingly, their results allowed for a natural string theory interpretation which independently suggests the emergence of superconnections in the anomaly formulas. Moreover, when the team applied these formulas to systems with interfaces and spacetime boundaries, they found that some of the known results for these systems were reproduced in a simple and unified manner.

The formalism developed in this study could be used to describe a broad range of topics in theoretical physics from quantum chromodynamics to topological matter with defects and boundaries, allowing us to explore deeper mathematical structures of physical theories that could lead us to realize new technologies.

]]>In quantum mechanics, electrons are described by wave forms, and thus, their wave functions are characterized by wave numbers in the Fourier space. Recently, the topological nature of the wave functions in the Fourier space (that is, momentum space) has been confirmed to provide various peculiar properties to materials, which are called “topological materials.” However, extracting the topological nature as an observable quantity in a bulk material is difficult. In this paper, we propose that spin current in an organic conductor is an appropriate physical quantity to detect the topological property of the material.

The organic conductors considered in this study are layered materials composed of relatively large molecules, and the electrons can move around hopping on various molecules forming a quasi-two-dimensional electron system. Material parameters such as the lattice constant, kinetic energy of electrons, and interaction between particles can be rather easily controlled by pressure or by substituting molecules with slightly different molecules. Consequently, organic conductors demonstrate various interesting properties as shown in a wide variety of phase diagrams of parameters. Recently, related to the topological nature, a certain class of organic conductors whose electrons obey the quasi-two-dimensional Dirac equation has been focused on. The Dirac equation was proposed by Dirac in 1928, which combined the newly born field of quantum mechanics and relativity. It predicts positrons occupying the vacuum. However, an electron–positron pair creation requires very high energy. In an organic conductor, α-(BETS)_{2}I_{3}, the first-principles band calculation shows that electrons inside obey an equation similar to the Dirac equation, but with a very small energy gap. Therefore, in this material, the corresponding electron–positron (called hole in solids) pair creation requires considerably less energy than that for the original electron–positron pair creation. It can be created using thermal energy even at room temperatures.

Theoretically, the two-dimensional Dirac electrons have been shown to have very peculiar topological properties. However, the conventional physical quantities are often written as an integral over the momentum space. Consequently, the topological nature of the Dirac electrons represented by Berry curvature vanishes after integration because the Berry curvature has two opposite-sign contributions at the two distinct Dirac points in the momentum space. In this study, we noticed that this cancellation can be avoided by considering spin current, and the topological nature of the Dirac electrons in α-(BETS)_{2}I_{3}
can be detected in the spin current that can be measured using recent experimental techniques. More explicitly, we calculated the spin Hall conductivity and spin conductivity in a magnetic field based on a linear response theory.

(written by Masao Ogata on behalf of all authors)

]]>The fluctuation-dissipation theorem (FDT) claims that the current fluctuation in a macroscopic equilibrium system is equal to the product of the temperature and electrical conductivity. This “theorem” was proved for classical systems for all components of fluctuations including off-diagonal fluctuations, namely cross-time correlations between currents flowing in different directions.

However, the validity of the FDT in quantum systems was questioned, because disturbances by quantum measurement often play a crucial role, which was ignored in the proof of the FDT for classical systems. Recently, this long-standing question was formally solved, and the FDT was shown to be violated even when the fluctuation is measured in a way that simulates the classical ideal measurement as closely as possible. However, this formal solution neither gave concrete systems that exhibit the FDT violation nor estimated the magnitude of violation.

We propose a two-dimensional electron system in a magnetic field as a real physical system in which the FDT is violated. We clarify the conditions for large violations and show that the magnitude of violation is macroscopically large. In fact, the FDT for the off-diagonal component is significantly violated in a strong magnetic field at low temperatures, whereas the FDT for the diagonal component holds for any values of the parameters. In the standard setup used in the quantum Hall effect experiments, the off-diagonal current fluctuation is several tens of times larger than the product of temperature and Hall conductivity (off-diagonal conductivity).

Such a large violation implies novel properties of off-diagonal current fluctuations that are yet to be studied. Localized states of electrons contribute to the off-diagonal current fluctuation to the same extent as extended states, and hence, the off-diagonal fluctuation is insensitive to system imperfections. This is in sharp contrast to the Hall conductivity that is very sensitive to the imperfections because only extended states contribute. Moreover, as an application of this finding, we propose a new method for estimating the electron number density by measuring the off-diagonal fluctuation. Because fluctuations are a cause of error and noise, our results are expected to provide fundamental design guidelines for applications.

(Written by K. Kubo, K. Asano, and A. Shimizu)

]]>Phase transitions, such as the melting of ice, occur at finite (nonzero) temperatures as the result of thermal fluctuations, which cease as the matter is cooled to absolute zero (*T = *0 K). However, even at 0 K, quantum fluctuations remain and cause another type of phase transition, called a quantum phase transition (QPT). QPT has been observed in many materials that are referred to as strongly correlated electron systems. Normally, QPT occurs only at 0 K and at a critical value of a parameter called the quantum critical point (QCP). At finite temperatures, the QCP is connected to the classical phase transition line. Therefore, QPT is believed to be unobserved at finite temperatures.

We discovered that liquid helium (^{4}He) confined in a nanoporous material exhibits a superfluid transition governed by quantum fluctuations, even at finite temperatures. Ordinary liquid helium undergoes a phase transition from a normal viscous liquid to an extraordinary phase, called a superfluid. In the superfluid state, helium loses its viscosity, which is analogous to the zero-resistance state of superconducting electrons in metals. When liquid helium is placed into the nanopores of a porous glass called Gelsil, it exhibits a zero-temperature QPT, in which the superfluid state disappears at a certain critical pressure. However, the phase transition line in the pressure–temperature diagram exhibits a behavior that is explained by quantum criticality.

Therefore, in this work, to investigate the quantum effect at nonzero temperatures, we carefully studied the superfluid transition at many pressures using a newly developed superfluid resonator apparatus. The resonator consists of two bulk helium reservoirs separated by nanoporous glass filled with helium. When helium in the nanopores becomes a superfluid, the liquid flows between the reservoirs, resulting in a change in the resonance characteristics of the entire apparatus. We can precisely obtain the flow properties that are controlled by the superfluid density (quantity of helium atoms participating in the superfluidity) and dissipation (energy loss by nonsuperfluid components). We found that the superfluid density obeys a temperature–distance power law from the transition temperature, and the power, which is called the critical exponent, is 1.0, at all pressures measured. A critical exponent of 1 indicates that the superfluid critical phenomenon in the nanopores belongs to the four-dimensional (4D) XY universality class. This is decisive evidence for quantum criticality at finite temperatures. In ordinary bulk helium, the critical exponent is 0.67, indicating that the transition is three-dimensional.

Why is the superfluid transition of the nano-confined helium 4D? It has already been revealed that the QPT at 0 K exhibits 4D (equal to three spatial dimensions plus one imaginary time dimension) XY characteristics. At finite temperatures, superfluidity is caused by the frequent movement of helium atoms in nanopores. However, this motion was strongly suppressed at many narrow bottlenecks in the porous structure. This interruption of atom motion induces a quantum fluctuation in the superfluid order. As a result, the critical behavior changes from classical to quantum, that is, to that of a 4D XY class.

In the resonator experiment, we observed dissipation below the superfluid transition temperature. This dissipation can also be explained by its quantum nature at finite temperatures. Above the transition, helium forms many nanoscale droplets of superfluid, which are called localized Bose–Einstein condensates (LBECs). Dissipation occurs during the growth of superfluidity by matching the phases of the LBECs. The agreement of the calculated dissipation with the experimental one also establishes the validity of the quantum nature at finite temperatures.

Theoretically, the 4D transition is the simplest phase transition that can be rigorously analyzed using mean-field theory, which is the most straightforward theory describing phase transitions. Interestingly, helium in such a complicated nanoporous structure undergoes the simplest phase transition in nature. Our findings support a basic understanding of both quantum and classical phase transitions. Further studies will reveal novel superfluid phenomena governed by the quantum nature of liquid He.

(Written by K. Shirahama on behalf of all authors)

]]>Nonlinear physics is an extensively studied field that is highlighted by the emergence of solitons and chaos. A soliton is a solitary wave that is stabilized by the nonlinear term. It is originally proposed in the surface wave of water and then found in various systems. The Toda lattice is a typical nonlinear model possessing an exact soliton solution. It is experimentally realized in a transmission line consisting of inductors and variable-capacitance diodes, where the variable-capacitance diodes provide the nonlinear elements. A stable voltage propagation was observed in this transmission line. In contrast, the topological physics is an emerging field, where characteristic topological edge states emerge in the topological phase. The Su–Schrieffer–Heeger (SSH) model is the simplest example of a topological insulator, where the bonds are alternating. To date, nonlinear and topological physics were studied independently. It is an interesting problem to study a nonlinear topological physics, which will open a new field of physics.

We generalize the Toda lattice to a dimerized Toda lattice as in the case of the SSH model. We show that this model is realized by changing the inductance alternately in the transmission line realizing the Toda lattice. This model has topological edge states although it is a nonlinear model. We verify it by investigating the quench dynamics, where we apply a voltage at the edge node and explore its time evolution. The voltage propagates freely along the chain in the trivial phase, whereas it remains at the edge node in the topological phase. Hence, the absence and the existence of the topological edge states are well signaled by the voltage propagation dynamics. Thus, nonlinear topological physics will be relatively easily realized and studied experimentally in electric circuits. This result will open a new field of nonlinear topological physics.

(Written by M. Ezawa)

]]>When voltage *V* is applied to the sample, electrical current *I* proportional to the voltage flows as *V* = *R *× *I* or *I* = *G *× *V*, where *R*
and *G* (= 1/*R*) denote the resistance and conductance, respectively. This is the well-known Ohm’s law, also called as the linear conduction because of a linear relationship between current *I* and voltage *V*.

In contrast, several materials show nonlinear conduction, in which current *I* is not proportional to voltage *V*. The representatives are the nonlinear semiconductor devices such as diodes and transistors, as widely used in modern electronics. Recently, nonlinear conduction has also been observed in various correlated insulators, and it becomes a challenging issue to clarify the underlying mechanism of the nonlinearity.

A peculiar class of the organic-molecular-based compounds hosts an emergent electron crystal called “charge order,” in which the electrons are arranged periodically owing to the Coulomb repulsion. It provides a fascinating playground to study the nonlinear conduction because such a charge crystal may be highly sensitive to the external electric field as the normal crystal is affected by the external mechanical force. Indeed, organic salt α-(ET)_{2}I_{3}, in which the charge order emerges at *T*_{CO} = 136 K, exhibits interesting nonlinear transport such as a collective sliding motion of charge order above the threshold field.

In the present study, the authors aim to examine the low-field nonlinear response of charge-ordered salt α-(ET)_{2}I_{3}
by a harmonic conductivity experiment. Generally, the nonlinear conduction can be expressed as a Taylor series of current *I* as *I* = *G*_{1}*V*
+ *G*_{2}*V*^{2} + *G*_{3}*V*^{3}
…, where *G _{i}*
denotes the

The authors note that the third-order conductance of α-(ET)_{2}I_{3}
is critically enhanced near the charge order transition temperature. As the origin, a close relation between the third-order conductance and the third-order electric susceptibility has been discussed. Thermodynamically, the third-order susceptibility may relate to a quadrupole moment; thus, the present results imply a quadrupole instability hidden in the charge-ordered organic salt.

Although the crystal structure of molecular-based compounds appears very complicating at the first glance, it is greatly simplified by regarding the complicated molecule as a point-like charge (electric monopole). The present results indicate that the asymmetric charge distribution in the molecule unit with a higher-order quadrupole moment is essential to thoroughly understand various intriguing properties of molecular solids.

(Written by R. Okazaki on behalf of all authors)

]]>Since the early 2020, governments across the globe have grappled with preventing the spread of COVID-19 and mitigating the economic impacts of this deadly virus. Several debates have raged over the methods to balance stringent infection control while maintaining a sense of economic normalcy.

In this study, theories of thermodynamics have been used to generate a new concept termed as "economic irreversibility." It contends that delaying infection control measures is additionally expensive in the long run.

Although, certain economists have utilized a cost-benefit analysis to argue for timely intervention, its universal applicability remains questionable. This is because previous studies have been performed using numerical simulations that include investigating specific situations with given parameters the results of which depend on the socio-economic conditions and on the characteristics of the infectious agents.

To further develop a universal guiding principle to control pandemics, the author’s experience in thermodynamics is utilized.

A cost-benefit analysis is an optimization problem similar to exploring more efficient thermal cycles in thermodynamics. The benefit and cost are the reduction in infections, and the economic damage caused by the countermeasure, respectively. The efficiency of the countermeasure processes are theoretically compared with the same period in which the initial and the final infection status (the number of infected persons) remain the same.

The application of economic irreversibility showed that the delay in infection control results in increased costs and contradicts the idea that infection control translates into economic damage. In terms of thermodynamics, it can be said that early countermeasures render the situation more reversible.

Furthermore, this study did not require adjusting for different infectious diseases or socio-economic conditions, making it applicable on a wider scale. It can be applied to the current COVID-19 pandemic or probable future ones, regardless of whether “herd immunity” exists or not. To the best of the author’s knowledge, this is the first analytical study of the economic efficiency during pandemic control.

The validity of the present study is subject to the assumptions of the methodology. In this study, two principal assumptions have been made:

1. |
The intervention cost depends on the effective reproduction number, and its cost function is concave as to the effective reproduction number. |

2. |
The epidemic is in the infection-spreading phase and thus the infected population increases and decreases while obeying exponential dynamics. |

It is assumed that countermeasures are utilized in order corresponding to their cost-effectiveness. Moreover, exponential dynamics is a common feature of pandemics. Thus, the results are not restricted to a specific model; however, they demonstrate the basic underlying characteristics of pandemic countermeasures.

(Written by T. Hondou)

]]>Gamma rays represent the most “energetic” electromagnetic waves in the electromagnetic spectrum, and are generated by some of the most violent events in the universe, such as supernova explosions. Additionally, gamma rays are emitted by energetic objects such as pulsars (spinning neutron stars) and quasars (luminous objects powered by supermassive black holes). Observing gamma rays can, therefore, provide key insights into the evolution of our universe.

Since gamma rays are absorbed by the atmosphere, they can only be observed by telescopes aboard space satellites or high-altitude balloons. The large area telescope on the Fermi Gamma-ray Space Telescope (Fermi-LAT) launched in 2008 was the latest telescope to detect gamma rays in the sub-GeV/GeV energy range. However, the angular resolution of the Fermi-LAT is not high enough to clearly distinguish the multiple gamma-ray sources observed at the Galactic Center (the rotational center of the Milky Way galaxy).

The Gamma-Ray Astro-Imager with Nuclear Emulsion (GRAINE) is a high-resolution gamma-ray telescope that aims to surmount this issue and make precise observations of gamma-ray sources. This balloon-borne telescope developed by Kobe University, Nagoya University, Okayama University of science, Aichi University of Education and Gifu University in Japan uses nuclear emulsion films (a type of photographic plate) and a large aperture area (10 m^{2}) to detect gamma rays in the energy range of 10 MeV-100 GeV.

When charged particles encounter a nuclear emulsion film, they leave behind tracks that can be examined under a microscope, allowing for high-resolution observations. In the case of GRAINE, the nuclear emulsion films detect gamma rays by tracking the position of electrons and positrons generated in pair production.

In 2018, researchers involved in the GRAINE project used the telescope to observe the Vela pulsar, the brightest known gamma-ray source, in collaboration with the Japan Aerospace Exploration Agency (JAXA), who launched the balloon. Along with gamma rays, protons and helium nuclei passed through the emulsion film during the observations. The hadronic interaction between these particles produced short-lived *π*^{0} particles that decayed into gamma rays.

In a new study, researchers developed a method to identify these interactions, which could be used to not only detect gamma rays but also calibrate their arrival direction, energy, polarization, and efficiency. Additionally, they developed a high-precision measurement system to automatically record the particle tracks captured on the films.

The proposed methods are expected to improve the imaging resolution of the telescope by two orders of magnitude, and could be implemented during the next balloon experiments with GRAINE to be launched by JAXA on 2023.

Thus far, AdS/CFT has been studied intensively in the large-*N* limit (*N* is an integer representing the size of the gauge group SU (*N*)), where the gauge theory is strongly coupled. In this study, I investigated AdS/CFT when *N* is finite and the gravitational theory is not weakly coupled.

It has been shown that even in this scenario, when quantum gravitational effects are important, some quantities related to topology and supersymmetry can still be calculated on the AdS side. In a similar vein, I calculated the superconformal index (SCI) of the *N* = 4 super-Yang-Mills theory (SYM), the maximally supersymmetric gauge theory.

I considered the duality between 4D 𝓝 = 4 SYM and the string theory in AdS_{5} x S^{5}. In the large-N limit, the supergravity contribution (through the plethystic exponential and single-particle index) on the AdS side was used to obtain the SCI.

When N is finite, both the quantum gravitational effect and the contribution of D3-branes become significant. Thus, the finite-N corrections for some quantities can be reproduced as the contribution of D-3 branes. I performed such a calculation to obtain the SCI with finite N on the AdS side.

I then compared the result to the known SCI calculated on the gauge theory side, and I confirmed that the finite-N corrections for higher-order terms could be correctly reproduced by the inclusion of wrapping D3-brane contributions.

It was recently discovered that it is possible to calculate the entropy of a black hole from the SCI. This method could, thus, provide a new approach to calculation of black hole entropy.

]]>At ambient pressure, water has three states depending on the temperature; gaseous (water vapor), liquid (water), and solid (ice) states. Below 0 °C, water freezes to form ice which comprises crystals with molecules arranged periodically. Electron spins, which are responsible for the magnetism of materials, have similar thermodynamic properties. In general magnets, the paramagnetic (gaseous) state is stable at high temperatures in which the electron spins have random directions, whereas when the temperature is lowered, a phase transition occurs at a certain critical temperature to the magnetically ordered (solid) state in which the electron spins exhibit a periodical alignment. The magnetically ordered (solid) state is, for instance, a ferromagnetic state in which all the electron spins are aligned in one direction or an antiferromagnetic state in which all the neighboring spins point in opposite directions. By controlling and utilizing these magnetic states, modern electronics has progressed exponentially. Recently, the "magnetic frustration" effect, which prevents such electron spins from forming a solid state, has been actively investigated, and the realization and potential applications of the spin liquid state which is "a liquid state of electron spins" caused by the frustration effect have garnered significant interest.

In a spin liquid state, the spins continue to fluctuate without freezing even at absolute zero. The most famous model of the spin liquid state is the resonant valence bond (RVB) state proposed by Nobel laureate P.W. Anderson in 1973, and its relevance to the mechanism of high-temperature superconductivity and the feasibility of quantum computing using fractional excitations and associated quantum entanglement of the spin liquid state. Therefore, the realization and clarification of the spin liquid state is one of the most important issues in modern physics.

The authors have focused on Ca-Kapellasite (CaCu_{3}(OH)_{6}Cl_{2}·0.6H_{2}O) as a model material for a quantum kagome antiferromagnet, which has a strong frustration and is expected to be an excellent candidate for the spin liquid state. The spin dynamics of this material has been investigated in detail down to the extremely low temperature of 82 mK through the μSR technique. It has been elucidated from the magnetization measurements that Ca-Kapellasite exhibits magnetic order at 7.2 K. Therefore, it appears to be a magnetic material that can be described by the mean-field approximation of classical spin systems. However, the proposed μSR experiments revealed that the spins were fluctuating even in the magnetically ordered state. This indicates the dynamic aspect of the magnetic state of a quantum kagome antiferromagnet. It is expected that the development of chemically modified samples and related materials, as well as precise measurements of the physical properties, will significantly advance the understanding of the physics of kagome spin liquids.

(Written by H. K. Yoshida on behalf of all authors)

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