scholarly journals The classical-quantum divergence of complexity in modelling spin chains

Quantum ◽  
2017 ◽  
Vol 1 ◽  
pp. 25 ◽  
Author(s):  
Whei Yeap Suen ◽  
Jayne Thompson ◽  
Andrew J. P. Garner ◽  
Vlatko Vedral ◽  
Mile Gu
Keyword(s):  
Stochastic Process ◽  
Quantum Mechanics ◽  
Complexity Science ◽  
Spin Chains ◽  
Quantum Mechanical ◽  
Quantum Model ◽  
Qualitative Behaviour ◽  
Ising Spin ◽  
Statistical Complexity ◽  
Classical Quantum

The minimal memory required to model a given stochastic process - known as the statistical complexity - is a widely adopted quantifier of structure in complexity science. Here, we ask if quantum mechanics can fundamentally change the qualitative behaviour of this measure. We study this question in the context of the classical Ising spin chain. In this system, the statistical complexity is known to grow monotonically with temperature. We evaluate the spin chain's quantum mechanical statistical complexity by explicitly constructing its provably simplest quantum model, and demonstrate that this measure exhibits drastically different behaviour: it rises to a maximum at some finite temperature then tends back towards zero for higher temperatures. This demonstrates how complexity, as captured by the amount of memory required to model a process, can exhibit radically different behaviour when quantum processing is allowed.

scholarly journals A glance beyond the quantum model

2009 ◽  
Vol 466 (2115) ◽  
pp. 881-890 ◽  
Author(s):  
Miguel Navascués ◽  
Harald Wunderlich
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Physical Theory ◽  
Quantum Mechanical ◽  
Quantum Model ◽  
Microscopic Structure ◽  
Quantum Mechanical System ◽  
Classical Physics ◽  
Quantum Limits ◽  
The Universe

One of the most important problems in physics is to reconcile quantum mechanics with general relativity, and some authors have suggested that this may be realized at the expense of having to drop the quantum formalism in favour of a more general theory. Here, we propose a mechanism to make general claims on the microscopic structure of the Universe by postulating that any post-quantum theory should recover classical physics in the macroscopic limit. We use this mechanism to bound the strength of correlations between distant observers in any physical theory. Although several quantum limits are recovered, such as the set of two-point quantum correlators, our results suggest that there exist plausible microscopic theories of Nature that predict correlations impossible to reproduce in any quantum mechanical system.

scholarly journals The day the universes interacted: quantum cosmology without a wave function

2019 ◽  
Vol 79 (9) ◽  
Author(s):  
A. V. Yurov ◽  
V. A. Yurov
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Cosmology ◽  
Quantum Mechanical ◽  
Quantum Model ◽  
Mechanical Interaction ◽  
Micro Scale ◽  
Friedmann Equations ◽  
Quantum Mechanical Effects ◽  
Phantom Fields

Abstract In this article we present a new outlook on the cosmology, based on the quantum model proposed by Michael and Hall (Phys Rev X 4(1–17):041013, 2014). In continuation of the idea of that model we consider finitely many classical homogeneous and isotropic universes whose evolutions are determined by the standard Einstein–Friedmann equations but that also interact with each other quantum-mechanically via the mechanism proposed in Michael and Hall [1]. The crux of the idea lies in the fact that unlike every other interpretation of the quantum mechanics, the Hall, Deckert and Wiseman model requires no decoherence mechanism and thus allows the quantum mechanical effects to manifest themselves not just on micro-scale, but on a cosmological scale as well. We further demonstrate that the addition of this new quantum-mechanical interaction lead to a number of interesting cosmological predictions, and might even provide natural physical explanations for the phenomena of “dark matter” and “phantom fields”.

Modelling Flexible Protein-Ligand Binding in p38α MAP Kinase using the QUBE Force Field

2019 ◽  
Author(s):  
Joshua Horton ◽  
Alice Allen ◽  
Daniel Cole
Keyword(s):  
Quantum Mechanics ◽  
Force Field ◽  
Map Kinase ◽  
Binding Free Energy ◽  
Quantum Mechanical ◽  
Enhanced Sampling ◽  
Relative Binding ◽  
Stringent Test ◽  
Flexible Protein ◽  
P38α Map Kinase

<div><div><div><p>The quantum mechanical bespoke (QUBE) force field is used to retrospectively calculate the relative binding free energy of a series of 17 flexible inhibitors of p38α MAP kinase. The size and flexibility of the chosen molecules represent a stringent test of the derivation of force field parameters from quantum mechanics, and enhanced sampling is required to reduce the dependence of the results on the starting structure. Competitive accuracy with a widely-used biological force field is achieved, indicating that quantum mechanics derived force fields are approaching the accuracy required to provide guidance in prospective drug discovery campaigns.</p></div></div></div>

scholarly journals IMPLICATIONS OF A QUANTUM MECHANICAL TREATMENT OF THE UNIVERSE

1998 ◽  
Vol 13 (05) ◽  
pp. 347-351 ◽  
Author(s):  
MURAT ÖZER
Keyword(s):  
Quantum Mechanics ◽  
Wave Packet ◽  
Early Universe ◽  
Mechanical Treatment ◽  
Correspondence Principle ◽  
Scale Factor ◽  
Quantum Mechanical ◽  
Quantum Mechanical Treatment ◽  
The Standard Model ◽  
The Universe

We attempt to treat the very early Universe according to quantum mechanics. Identifying the scale factor of the Universe with the width of the wave packet associated with it, we show that there cannot be an initial singularity and that the Universe expands. Invoking the correspondence principle, we obtain the scale factor of the Universe and demonstrate that the causality problem of the standard model is solved.

scholarly journals QUANTUM SINGULARITIES IN STATIC SPACETIMES

2011 ◽  
Vol 20 (05) ◽  
pp. 729-743 ◽  
Author(s):  
JOÃO PAULO M. PITELLI ◽  
PATRICIO S. LETELIER
Keyword(s):  
Quantum Mechanics ◽  
Wave Operator ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Mathematical Framework ◽  
Physical Content ◽  
Dirac Equations ◽  
Quantum Particles ◽  
Klein Gordon ◽  
Quantum Singularities

We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets satisfying Klein–Gordon and Dirac equations. We show that in many cases the classical singularities are excluded when tested by quantum particles but unfortunately there are other cases where the singularities remain from the quantum mechanical point of view. When it is possible we also find, for spacetimes where quantum mechanics does not exclude the singularities, the boundary conditions necessary to turn the spatial portion of the wave operator to be self-adjoint and emphasize their importance to the interpretation of quantum singularities.

On the error of approximations in quantum mechanics. I. General theory

1965 ◽  
Vol 257 (1081) ◽  
pp. 309-326 ◽  
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Computer Applications ◽  
Quantum Mechanical ◽  
Quantum Mechanical Calculations ◽  
Density Matrices ◽  
Single Error

General formulas for estimating the errors in quantum-mechanical calculations are given in the formalism of density matrices. Some properties of the traces of matrices are used to simplify the estimating and to indicate a way of obtaining a better approximation. It is shown that the simultaneous correction of all the equations to be fulfilled leads in most cases to a faster convergence than the exact fulfilment of some of the equations and approximating stepwise to some of the others. The corrective formulas contain only direct operations of the matrices occurring and so they are advantageous in computer applications. In the last section a ‘subjective error’ definition is given and by taking into account the weight of the errors of the several equations a faster convergence and a single error quantity is obtained. Some special applications of the method will be published later.

Quanta of the Third Kind

2021 ◽  
Vol 6 (3) ◽  
Author(s):  
Frank Wilczek
Keyword(s):  
Quantum Mechanics ◽  
Experimental Results ◽  
Quantum Mechanical ◽  
The Third

Quantum mechanics is nearly one hundred years old; and yet the challenge it presents to the imagination is so great that scientists are still coming to terms with some of its most basic implications. Theoretical insights and recent experimental results in anyon physics are leading physicists to revise and expand their ideas about what quantum-mechanical particles are and how they behave.

Extended Quantum Model for Porous Silicon Formation

1994 ◽  
Vol 358 ◽  
Author(s):  
H. Münder ◽  
St. Frohnhoff ◽  
M.G. Berger ◽  
M. Marso ◽  
M. Thönissen ◽  
...  
Keyword(s):  
Porous Silicon ◽  
Doping Level ◽  
Tunneling Probability ◽  
Quantum Mechanical ◽  
Quantum Model ◽  
Electrochemical Dissolution ◽  
Quantum Mechanical Calculations ◽  
Model Calculations ◽  
Etching Parameters ◽  
Substrate Doping

ABSTRACTThe formation of porous silicon (PS) by electrochemical dissolution of bulk Si is described by a new model involving quantum mechanical calculations of the tunneling probability of holes through small crystallites (< 60 Å) into the electrolyte. This tunneling probability shows oscillations as a function of crystallite size. The presented model calculations are in agreement to the microstructure of p-PS — deduced from Raman measurements — as a function of etching parameters and substrate doping level.

scholarly journals An analysis on Quantum mechanical Stability of Regular Polygons on a Point Base Using Heisenberg Uncertainty Principle

2021 ◽  
Vol 9 (10) ◽  
pp. 74-79
Author(s):  
Anurag Chapagain
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Stability Problem ◽  
Classical Mechanics ◽  
Quantum Mechanical ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
Degree Of Stability ◽  
The Stability ◽  
Heisenberg's Uncertainty Principle

Abstract: It is a well-known fact in physics that classical mechanics describes the macro-world, and quantum mechanics describes the atomic and sub-atomic world. However, principles of quantum mechanics, such as Heisenberg’s Uncertainty Principle, can create visible real-life effects. One of the most commonly known of those effects is the stability problem, whereby a one-dimensional point base object in a gravity environment cannot remain stable beyond a time frame. This paper expands the stability question from 1- dimensional rod to 2-dimensional highly symmetrical structures, such as an even-sided polygon. Using principles of classical mechanics, and Heisenberg’s uncertainty principle, a stability equation is derived. The stability problem is discussed both quantitatively as well as qualitatively. Using the graphical analysis of the result, the relation between stability time and the number of sides of polygon is determined. In an environment with gravity forces only existing, it is determined that stability increases with the number of sides of a polygon. Using the equation to find results for circles, it was found that a circle has the highest degree of stability. These results and the numerical calculation can be utilized for architectural purposes and high-precision experiments. The result is also helpful for minimizing the perception that quantum mechanical effects have no visible effects other than in the atomic, and subatomic world. Keywords: Quantum mechanics, Heisenberg Uncertainty principle, degree of stability, polygon, the highest degree of stability

scholarly journals Generation of Time-Independent and Time-Dependent Harmonic Oscillator-Like Potentials Using Supersymmetric Quantum Mechanics

2018 ◽  
Vol 4 (1) ◽  
pp. 47-55
Author(s):  
Timothy Brian Huber
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Mechanical System ◽  
Schrodinger Equation ◽  
Supersymmetric Quantum Mechanics ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Quantum Mechanical System ◽  
Intertwining Operator

The harmonic oscillator is a quantum mechanical system that represents one of the most basic potentials. In order to understand the behavior of a particle within this system, the time-independent Schrödinger equation was solved; in other words, its eigenfunctions and eigenvalues were found. The first goal of this study was to construct a family of single parameter potentials and corresponding eigenfunctions with a spectrum similar to that of the harmonic oscillator. This task was achieved by means of supersymmetric quantum mechanics, which utilizes an intertwining operator that relates a known Hamiltonian with another whose potential is to be built. Secondly, a generalization of the technique was used to work with the time-dependent Schrödinger equation to construct new potentials and corresponding solutions.

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