This paper provides a construction of a quantum statistical mechanical system associated to knots in the 3-sphere and cyclic branched coverings of the 3-sphere, which is an analog, in the sense of arithmetic topology, of the Bost-Connes system, with knots replacing primes, and cyclic branched coverings of the 3-sphere …
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48 results for “quantum mechanical properties”
4-manifolds have special topological properties which can be used to get a different view on quantum mechanics. One important property (connected with exotic smoothness) is the natural appearance of 3-manifold wild embeddings (Alexanders horned sphere) which can be interpreted as quantum states. This relation can be co…
A new constructivist approach to modeling in economics and theory of consciousness is proposed. The state of elementary object is defined as a set of its measurable consumer properties. A proprietor's refusal or consent for the offered transaction is considered as a result of elementary economic measurement. We were al…
Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctionsphysics.chem-ph
Machine learning advances chemistry and materials science by enabling large-scale exploration of chemical space based on quantum chemical calculations. While these models supply fast and accurate predictions of atomistic chemical properties, they do not explicitly capture the electronic degrees of freedom of a molecule…
We present an axiomatic modification of quaternionic quantum mechanics with a possible-worlds semantics capable of predicting essential "nonquantum" features of an observable universe model - the dimensionality and topology of spacetime, the existence, the signature and a specific form of a metric on it, and certain na…
Coherent manifoldsmath-ph
Defines coherent manifolds and their quantum applications.
problem Understanding quantum spaces and coherent states.
method Generalizes quantum field theory and Schrödinger equation solutions.
result Solves Schrödinger equation on coherent manifolds.
Study topological quantum mechanics on orbifolds with geometric interpretation.
problem Quantum mechanical models on symplectic orbifolds.
method Explicit orbifold version of quantum HKR map and exact semi-classical approximation.
result Geometric and quantum field theoretic interpretation of orbifold algebraic index.
Quantum mechanics models for financial Black-Scholes model.
problem Modeling financial derivatives using quantum mechanics.
method Noncommutative quantum mechanics applied to specific mechanical systems.
result Generalized noncommutative quantum mechanics of financial models.
Examines quantum mechanics equivalence with Newtonian geometry.
problem Equivalence principle in quantum mechanics.
method Newton--Cartan geometry, non--relativistic twistor theory.
result Discusses equivalence in quantum mechanics.
On Quantum Indeterminacyquant-ph
Unified geometric approach to quantum indeterminacy.
problem Quantum indeterminacy and uncertainty principles.
method Geometric formulation using convex geometry and symplectic topology.
result Robertson-Schrodinger inequalities emerge as geometric principles.
Novel RL approach for molecular design using quantum mechanics.
problem Existing RL methods for molecular design are limited in scope and reward function.
method Formulation in Cartesian coordinates, direct use of quantum mechanics for reward function, translation and rotation invariant state-action space.
result Agent efficiently learns to solve molecular design tasks from scratch.
The paper studies distributions and controllability in quantum mechanical systems.
problem Controlling quantum mechanical systems and their evolution.
method Analysis of distributions, controllability, and geodesics on sub-Finsler manifolds.
result Proves the Lie group decomposition and geodesics equivalence for quantum system steering.
This paper is an attempt at understanding the quantum-like dynamics of financial markets in terms of non-differentiable price-time continuum having fractal properties. The main steps of this development are the statistical scaling, the non-differentiability hypothesis, and the equations of motion entailed by this hypot…
A quantum system can be entirely described by the Kähler structure of the projective space P(H) associated to the Hilbert space H of possible states; this is the so-called geometrical formulation of quantum mechanics. In this paper, we give an explicit link between the geometrical formulation (of finite dimensional qua…
These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics and quantum field theory from a functional integral point of view, where the mai…
Complex analysis techniques link Gaussian RBF kernels to quantum mechanics.
problem Understanding the Gaussian RBF kernel in machine learning and SVMs.
method Using Fock space and Segal-Bargmann theories in complex analysis.
result Proves connections between Gaussian RBF kernels and quantum mechanics operators.
Study symmetry breaking in quantum mechanics to understand many-body physics.
problem Understanding many-body physics from quantum mechanics.
method Analyzing potentials with unstable critical points and local minima.
result Emergence of many-body physics from spontaneous symmetry breaking.
Quantum Econophysicsphysics.soc-ph
The relationships between game theory and quantum mechanics let us propose certain quantization relationships through which we could describe and understand not only quantum but also classical, evolutionary and the biological systems that were described before through the replicator dynamics. Quantum mechanics could be…
The submanifold quantum mechanics was opened by Jensen and Koppe (Ann. Phys. {\bf 63} (1971) 586-591) and has been studied for these three decades. This article gives its more algebraic definition and show what is the essential of the submanifold quantum mechanics from an algebraic viewpoint.
Quantum systems learn like machine learning models, influenced by dissipation.
problem Understanding how quantum systems learn and evolve.
method Hydrodynamical formulation of quantum mechanics, gradient descent model, empirical demonstration.
result Quantum systems follow a disrupted gradient descent model, influenced by dissipation.
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics …
Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Seriesquant-ph
Quantum algorithm samples from SDEs using DQCs and quantile mechanics.
problem Sampling from solutions of stochastic differential equations.
method Differentiable quantum circuits (DQCs) encoding latent variables, quantile mechanics.
result Quantum algorithm generates time-series from SDEs.
Binary operations on algebras of observables are studied in the quantum as well as in the classical case. It is shown that certain natural compatibility conditions with the associative product imply the properties which usually are additionally required. In particular, it is proved that locality of a Loday bracket on s…
Paper introduces a new deep-learning method for quantum mechanics.
problem Simulating time-evolving Schrödinger equations efficiently.
method Generative diffusion models and stochastic mechanics.
result Significantly lower computational complexity compared to existing methods.
We compare the covariant formulation of Quantum Mechanics on a curved spacetime fibred on absolute time with the standard Geometric Quantisation.
The probability distribution function (PDF) for prices on financial markets is derived by extremization of Fisher information. It is shown how on that basis the quantum-like description for financial markets arises and different financial market models are mapped by quantum mechanical ones.
A Theory of Complex Adaptive Learning and a Non-Localized Wave Equation in Quantum Mechanicsq-fin.GN
The abstract explores a new wave equation linking quantum mechanics and complex adaptive systems.
problem Understanding the underlying mechanism of distribution formation in complex quantum entanglement.
method Exploring the logical relationship between Schrödinger's wave equation and Shi's trading volume-price wave equation in finance.
result A non-localized wave equation in quantum mechanics reveals the invariance of interaction as a universal law.
The abstract discusses connecting quantum mechanics and algebraic index theories.
problem Exploring the connection between quantum mechanics and algebraic index theories.
method Explains how the classical algebraic index theorem can be proved in terms of BV quantization of topological quantum mechanics and 2d chiral CFT.
result Shows how the generating function of all genus Gromov-Witten invariants on elliptic curves is mirror equivalent to an elliptic chiral index.
De la structure des espaces fibrés aux équations fondamentales de la physique. Une introductionphysics.class-ph
This text explains how fiber bundle structure is fundamental for classical physics.
problem None explicitly stated, but implied as understanding fiber bundles is crucial for physics.
method Explains the fiber bundle structure and its universality for physics laws.
result Fiber bundle structure is fundamental for classical physics laws.
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is governed via (a kind of) a parallel transport in this bundle. Some problems concernin…
A new graph model HMG and neural network HMGNN improve molecule property predictions.
problem Predicting quantum mechanical properties of molecules with limited consideration of many-body interactions.
method Introducing heterogeneous molecular graphs (HMG) and building HMGNN on neural message passing scheme.
result HMGNN achieves state-of-the-art performance in 9 out of 12 tasks on the QM9 dataset.
Eigen component analysis combines quantum mechanics with machine learning for efficient data analysis.
problem Efficiently extracting linearly separable components from complex data.
method Eigen component analysis (ECA) incorporates quantum mechanics principles into linear learning models.
result ECA outperforms classical linear models and can be integrated with deep neural networks.
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum s…
Torus quantum vortex knots in the Gross-Pitaevskii model for Bose-Einstein condensatescond-mat.quant-gas
We examine on the static and dynamical properties of quantum knots in a Bose-Einstein condensate. In particular, we consider the Gross-Pitaevskii model and revise a technique to construct ab initio the condensate wave-function of a generic torus knot. After analysing its excitation energy, we study its dynamics relatin…
Statistical Mechanics Calculations Using Variational Autoregressive Networks and Quantum Annealingcond-mat.dis-nn
New method uses quantum annealing and VAN for better statistical mechanics calculations.
problem Difficulty in computing partition function in statistical mechanics.
method Combines quantum annealing samples with variational autoregressive networks.
result Enhanced accuracy in finite-size Sherrington-Kirkpatrick model.
We give an exposition, following joint works with J.-C. Zambrini, of the link between Euclidean Quantum Mechanics, Bernstein processes and isovectors for the heat equation. A new application to Mathematical Finance is then discussed.
Study asymptotics of unitary matrix elements in quantum mechanics.
problem Asymptotic behavior of unitary matrix elements in quantum mechanics.
method Uses Berezin-Toeplitz quantization and symplectic geometry.
result Recover asymptotics of Wigner's d-matrix elements for spin representations.
Quantum reservoir computing needs coherence influx for effective information processing.
problem Understanding and optimizing quantum reservoir computing.
method Theoretical and numerical analysis of quantum systems, focusing on coherence influx and spectral radius of Pauli transfer matrix.
result Coherence influx is essential for realizing nonstationary echo state property in quantum reservoir computing.
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle probabilistic predictions of observables. After introducing the geometric theory of Ha…
Quantum Mechanics, Path Integrals and Option Pricing: Reducing the Complexity of Financecond-mat.soft
Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some of the methods of lattice simulations of path integrals for the pricing of optio…
Quantum mechanics models human perception and decision-making, offering a new approach to understanding social dynamics.
problem Understanding the complex interactions between individuals and groups in social networks.
method Developed a simple computational code based on quantum mechanics principles to model human perception and decision-making.
result Quantum-inspired models can help explain differences in individual and group behavior.
A multi-scale model predicts atomic-scale properties using both local and long-range information.
problem Inability of machine-learning schemes to capture long-range physical effects.
method Combines local and non-local information in a multipole expansion framework.
result Demonstrates the ability to model electrostatics, polarization, and dispersion.
Quantum learning complexity reviewed using information theory.
problem Learning properties of quantum systems or processing data via quantum computing.
method Information-theoretic techniques focusing on data, copy, and model complexity.
result Copy complexity due to irreversible quantum measurements limits information extraction.
Automates GNN design for molecular property prediction.
problem Designing and tuning GNN architectures for molecular property prediction is labor-intensive.
method Developed a NAS approach to automatically discover high-performing GNN architectures for MPNNs.
result Automatically discovered MPNNs outperform manually designed GNNs in molecular property prediction.
Quantum method improves CVaR evaluation under correlated fields.
problem Accurately evaluating CVaR in high-dimensional, correlated material uncertainty.
method Quantum-enhanced inference framework using stabilized IQAE.
result Quantum method achieves lower oracle complexity than classical methods.
Quantum classification robustness improved via quantum hypothesis testing.
problem Vulnerability of quantum classification algorithms to input perturbations.
method Formalized link between quantum hypothesis testing and robustness, developed practical protocols.
result Tight robustness condition independent of noise source (natural or adversarial).
Quantum tech speeds up financial risk assessment.
problem Improving credit valuation adjustments using quantum mechanics.
method Developed a quantum algorithm using Bayesian quantum amplitude estimation and engineered likelihood functions.
result Significant speedup in quantum computations for CVA over classical methods.
Econophysics has developed as a research field that applies the formalism of Statistical Mechanics and Quantum Mechanics to address Economics and Finance problems. The branch of Econophysics that applies of Quantum Theory to Economics and Finance is called Quantum Econophysics. In Finance, Quantum Econophysics' contrib…