Lagrange formalism of memory circuit elements: classical and quantum formulations

Abstract

The general Lagrange-Euler formalism for the three memory circuit elements, namely, memristive, memcapacitive, and meminductive systems, is introduced. In addition, {\it mutual meminductance}, i.e. mutual inductance with a state depending on the past evolution of the system, is defined. The Lagrange-Euler formalism for a general circuit network, the related work-energy theorem, and the generalized Joule's first law are also obtained. Examples of this formalism applied to specific circuits are provided, and the corresponding Hamiltonian and its quantization for the case of non-dissipative elements are discussed. The notion of {\it memory quanta}, the quantum excitations of the memory degrees of freedom, is presented. Specific examples are used to show that the coupling between these quanta and the well-known charge quanta can lead to a splitting of degenerate levels and to other experimentally observable quantum effects.

References in corpus (6)

• Memory effects in complex materials and nanoscale systems
• Solving mazes with memristors: a massively-parallel approach
• Bistable non-volatile elastic membrane memcapacitor exhibiting chaotic behavior
• Chaotic memristor
• Quantum Effects in Small-Capacitance Single Josephson Junctions
• The elastic capacitor and its unusual properties

Cited by in corpus (10)

• On the physical properties of memristive, memcapacitive, and meminductive systems
• Quantum Memristors
• Qubit-based memcapacitors and meminductors
• Quantum Memristors in Frequency-Entangled Optical Fields
• Reading, writing and squeezing the entangled states of two nanomechanical resonators coupled to a SQUID
• Quantized Single-Ion-Channel Hodgkin-Huxley Model for Quantum Neurons
• Quantized Three-Ion-Channel Neuron Model for Neural Action Potentials
• Circuit proposition for copying the value of a resistor into a memristive device supported by HSPICE simulation
• Classical and Quantum Stochastic Models of Resistive and Memristive Circuits
• Spike and Tyke, the Quantized Neuron Model