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A quantum device simulating the human decision making process is introduced. It consists of quantum recurrent nets generating stochastic processes which represent the motor dynamics, and of classical neural nets describing the evolution of probabilities of these processes which represent the mental dynamics.
Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems.
We launched a combined negative ion photoelectron spectroscopy and multiscale theoretical investigation on the geometric and electronic structures of a series of acetonitrile-solvated dodecaborate clusters, i.e., B 12 H 12 2- ·nCH 3 CN (n = 1–4). The electron binding energies of B 12 H 12 2- ·nCH 3 CN are observed to increase with cluster size, suggesting their enhanced electronic stability. B3LYP-D3(BJ)/ma-def2-TZVP geometry optimizations indicate each acetonitrile molecule binds to B 12 H 12 2- via a threefold dihydrogen bond (DHB) B3–H3 ⋮⋮⋮ H3C–CN unit, in which three adjacent nucleophilic H atoms in B 12 H 12 2- interact with the three methyl hydrogens of acetonitrile. The structural evolution from n = 1 to 4 can be rationalized by the surface charge redistributions through the restrained electrostatic potential analysis. Notably, a super-tetrahedral cluster of B 12 H 12 2- solvated by four acetonitrile molecules with 12 DHBs is observed. The post-Hartree–Fock domain-based local pair natural orbital- coupled cluster singles, doubles, and perturbative triples [DLPNO-CCSD(T)] calculated vertical detachment energies agree well with the experimental measurements, confirming the identified isomers as the most stable ones. Furthermore, the nature and strength of the intermolecular interactions between B 12 H 12 2- and CH 3 CN are revealed by the quantum theory of atoms-in-molecules and the energy decomposition analysis. Ab initio molecular dynamics simulations are conducted at various temperatures to reveal the great kinetic and thermodynamic stabilities of the selected B 12 H 12 2- ·CH 3 CN cluster. The binding motif in B 12 H 12 2- ·CH 3 CN is largely retained for the whole halogenated series B 12 X 12 2- ·CH 3 CN (X = F–I). This study provides a molecular-level understanding of structural evolution for acetonitrile-solvated dodecaborate clusters and a fresh view by examining acetonitrile as a real hydrogen bond (HB) donor to form strong HB interactions.
This review focuses on diffractive physics, which involves the long-range interactions of strong nuclear force at high energies described by SU(3) gauge symmetry. It is expected that diffractive processes account for nearly 40% of the total cross-section at LHC energies. These processes consist of soft-scale physics where perturbation theory cannot be applied. Although highly successful and often described as a perfect theory, quantum chromodynamics relies heavily on perturbation theory, a model best suited for hard-scale physics. The study of pomerons could help bridge the soft and hard processes and provide a complete description of the theory of the strong interaction across the full momentum spectrum. Here, we will discuss some of the features of diffractive physics, experimental results from SPS, HERA, and the LHC, and where the field could potentially lead. With the recent publication of the odderon discovery in 2021 by the D0 and TOTEM collaborations and the new horizon of physics that lies ahead with the upcoming Electron-Ion Collider at Brookhaven National Laboratory, interest is seemingly piquing in high energy diffractive physics.
If holography is an equivalence between quantum theories, one might expect it to be described by a map that is a bijective isometry between bulk and boundary Hilbert spaces, preserving the hamiltonian and symmetries. Holography has been believed to be a property of gravitational (or string) theories, but not of non-gravitational theories; specifically Marolf has argued that it originates from the gauge symmetries and constraints of gravity. These observations suggest study of the assumed holographic map as a function of the gravitational coupling G . The zero coupling limit gives ordinary quantum field theory, and is therefore not necessarily expected to be holographic. This, and the structure of gravity at non-zero G , raises important questions about the full map. In particular, construction of a holographic map appears to require as input a solution of the nonperturbative analog of the bulk gravitational constraints, that is, the unitary bulk evolution. Moreover, examination of the candidate boundary algebra, including the boundary hamiltonian, reveals commutators that don’t close in the usual fashion expected for a boundary theory.
Optimum signal reception using quantum-mechanical communication theory
Extension of SU/6/ symmetry to relativistic quantum theory to produce intrinsically broken U/6/xU/6/ symmetry for strong interactions
The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely theoretically unexplored due to inadequacy of Monte-Carlo–based computational techniques in overcoming a sign problem. Quantum computing offers a sign-problem-free approach, but evaluating thermal expectation values is generally resource intensive on quantum computers. To facilitate thermodynamic studies of gauge theories, we propose a generalization of the thermal-pure-quantum-state formulation of statistical mechanics applied to constrained gauge-theory dynamics, and numerically demonstrate that the phase diagram of a simple low-dimensional gauge theory is robustly determined using this approach, including mapping a chiral phase transition in the model at finite temperature and chemical potential. Quantum algorithms, resource requirements, and algorithmic and hardware error analysis are further discussed to motivate future implementations. Thermal pure quantum states, therefore, may present a suitable candidate for efficient thermal simulations of gauge theories in the era of quantum computing.
The Quantum Null Energy Condition (QNEC) is a lower bound on the stress-energy tensor in quantum field theory that has been proved quite generally. It can equivalently be phrased as a positivity condition on the second null shape derivative of the relative entropy S rel (ρ||σ) of an arbitrary state ρ with respect to the vacuum σ. The relative entropy has a natural one-parameter family generalization, the Sandwiched Rényi divergence S n (ρ||σ), which also measures the distinguishability of two states for arbitrary n ∈ [1/2, ∞). A Rényi QNEC, a positivity condition on the second null shape derivative of S n (ρ||σ), was conjectured in previous work. In this work, we study the Rényi QNEC for free and superrenormalizable field theories in spacetime dimension d > 2 using the technique of null quantization. In the above setting, we prove the Rényi QNEC in the case n > 1 for arbitrary states. We also provide counterexamples to the Rényi QNEC for n < 1.
In this paper, we develop an exact analytical quantum theory for field emission from surfaces with a nearby quantum well, by solving the one-dimensional time-independent Schrödinger equation. The quantum well, which may be introduced by ions, atoms, nanoparticles, etc., is simplified as a square potential well with depth H, width d, and distance to the surface L. The theory is used to analyze the effects of the quantum well (d, H, and L), the cathode properties (work function W and Fermi energy E F ), and dc field F. It is found that the quantum well can lead to resonant tunneling enhanced field emission up to several orders of magnitude larger than that from bare cathode surfaces. In the meantime, the electron-emission-energy spectrum is significantly narrowed. The strong enhancement region is bounded by the conditions eFL + H ≥ W + C and eFL ≤ W, with e being the elementary charge (positive) and C a constant dependent on dc field F. It is also found that the linear shift of resonance peaks in the electron-emission-energy spectrum with dc field F follows ε p =ε p0 –eFL, with ε p0 being approximately the eigenenergies for electrons confined in a square potential well without a dc field. Finally, the theory provides insights for the design of high-efficiency field emitters, which can produce a high current and highly collimated electron beams.
We discuss a large class of classical field theories with continuous translation symmetry. In the quantum theory, a new anomaly explicitly breaks this translation symmetry to a discrete symmetry. Furthermore, this discrete translation symmetry is extended by a d – 2-form global symmetry. All these theories can be described as U(1) gauge theories where Gauss law states that the system has nonzero charge density. Special cases of such systems can be phrased as theories with a compact phase space. Examples are ferromagnets and lattices in the lowest Landau level. In some cases, the broken continuous translation symmetry can be resurrected as a noninvertible symmetry. We clarify the relation between the discrete translation symmetry of the continuum theory and the discrete translation symmetry of an underlying lattice model. Our treatment unifies, clarifies, and extends earlier works on the same subject.
Quantum theory to investigate ferromagnetic metals - interaction of Fermi excitations with spin waves and temperature effect on thermodynamic quantities
Rate coefficient derived for derived for dielectronic recombination using quantum theory of resonance collision processes
For very low noise millimeter-wave receivers, the superconductor-insulator-superconductor (SIS) quasiparticle mixer is now competitive with conventional Schottky mixers. Tucker (1979, 1980) has developed a quantum theory of mixing which has provided a basis for the rapid improvement in SIS mixer performance. The present paper is concerned with a general method of numerical analysis for SIS mixers which allows arbitrary terminating impedances for all the harmonic frequencies. This analysis provides an approach for an examination of the range of validity of the three-frequency results of the quantum mixer theory. The new method has been implemented with the aid of a Fortran computer program.
Einstein’s general theory of relativity from 1915 remains the most successful description of gravitation. From the 1919 solar eclipse to the observation of gravitational waves, the theory has passed many crucial experimental tests. However, the evolving concepts of dark matter and dark energy illustrate that there is much to be learned about the gravitating content of the universe. Singularities in the general theory of relativity and the lack of a quantum theory of gravity suggest that our picture is incomplete. It is thus prudent to explore gravity in exotic physical systems. Antimatter was unknown to Einstein in 1915. Dirac’s theory appeared in 1928; the positron was observed in 1932. There has since been much speculation about gravity and antimatter. The theoretical consensus is that any laboratory mass must be attracted by the Earth, although some authors have considered the cosmological consequences if antimatter should be repelled by matter. In the general theory of relativity, the weak equivalence principle (WEP) requires that all masses react identically to gravity, independent of their internal structure. Here we show that antihydrogen atoms, released from magnetic confinement in the ALPHA-g apparatus, behave in a way consistent with gravitational attraction to the Earth. Repulsive ‘antigravity’ is ruled out in this case. This experiment paves the way for precision studies of the magnitude of the gravitational acceleration between anti-atoms and the Earth to test the WEP.
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It is currently understood that there are four fundamental forces in nature: gravitational, electromagnetic, weak and strong forces. The strong force governs the interactions between quarks and gluons, elementary particles whose interactions give rise to the vast majority of visible mass in the universe. The mathematical description of the strong force is provided by the non-Abelian gauge theory Quantum Chromodynamics (QCD). While QCD is an exquisite theory, constructing the nucleons and nuclei from quarks, and furthermore explaining the behavior of quarks and gluons at all energies, remain to be complex and challenging problems. Such challenges, along with the desire to understand all visible matter at the most fundamental level, position the study of QCD as a central thrust of research in nuclear science. Experimental insight into the strong force can be gained using large particle accelerator facilities, which are necessary to probe the very short distance scales over which quarks and gluons interact. The Long Range Plans (LRPs) exercise of 1989 and 1996 led directly to the construction of two world-class facilities: the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab (JLab) that is focused on studying how the structure of hadrons emerges from QCD (cold QCD research), and the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Lab (BNL) that aims at the discovery and study of a new state of matter, the quark-gluon plasma (QGP), at extremely high temperatures (hot QCD research). These past investments have produced major advances. Nucleons and nuclei are being studied with increasing precision with a unified description of the partonic structure utilizing multi-dimensional imaging. Significant progress has been made, paving the way towards a complete picture of how quarks and gluons give rise to the mass, spin, and momentum of the nucleon. In hot QCD, the QGP is created in the collisions of nuclei at RHIC and the Large Hadron Collider (LHC) and is observed to behave like a fluid with very low specific shear viscosity; the current goals are to understand how the fluid behavior emerges from QCD and to characterize the temperature (and chemical potential) dependence of the properties of the QGP. As this White Paper is written, current experimental programs at CEBAF, RHIC and the LHC continue to provide exciting near term opportunities to capitalize on the investments in experimental equipment and accelerator operations. Most importantly, the QCD community looks forward to the construction of the Electron Ion Collider (EIC) as a major new facility to push forward QCD research in the next decades, with significant focus on exploring the properties of gluons, the mediators of the strong force.
A canonical quantization procedure is applied to the interaction of elastic waves—phonons—with infinitely long dislocations that can oscillate about an equilibrium, straight line, configuration. The interaction is implemented through the well-known Peach–Koehler force. For small dislocation excursions away from the equilibrium position, the quantum theory can be solved to all orders in the coupling constant. We study in detail the quantum excitations of the dislocation line and its interactions with phonons. The consequences for the drag on a dislocation caused by the phonon wind are pointed out. We compute the cross-section for phonons incident on the dislocation lines for an arbitrary angle of incidence. The consequences for thermal transport are explored, and we compare our results, involving a dynamic dislocation, with those of Klemens and Carruthers, involving a static dislocation. In our case, the relaxation time is inversely proportional to frequency, rather than directly proportional to frequency. As a consequence, the thermal transport anisotropy generated on a material by the presence of a highly-oriented array of dislocations is considerably more sensitive to the frequency of each propagating mode, and, therefore, to the temperature of the material.