Related Experiment Video
Updated: Nov 27, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Unification of the Nature's Complexities via a Matrix Permanent-Critical Phenomena, Fractals, Quantum Computing,
Vitaly Kocharovsky1,2, Vladimir Kocharovsky2, Sergey Tarasov2
1Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242, USA.
Abstract:
We reveal the analytic relations between a matrix permanent and major nature's complexities manifested in critical phenomena, fractal structures and chaos, quantum information processes in many-body physics, number-theoretic complexity in mathematics, and ♯P-complete problems in the theory of computational complexity. They follow from a reduction of the Ising model of critical phenomena to the permanent and four integral representations of the permanent based on (i) the fractal Weierstrass-like functions, (ii) polynomials of complex variables, (iii) Laplace integral, and (iv) MacMahon master theorem.
Related Concept Videos
Parallel Processing
Fundamental Theorem of Algebra
Ampere-Maxwell's Law: Problem-Solving
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of the...
The Wave Nature of Light
Multimachine Stability
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
Cyclic Processes And Isolated Systems
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each...

