Statistical Mechanics and Thermodynamics: Boltzmann’s versus Planck’s State Definitions and Counting

During the physical foundation of his radiation formula in his December 1900 talk and subsequent 1901 article, Planck refers to Boltzmann’s 1877 combinatorial-probabilistic treatment and obtains his quantum distribution function, while Boltzmann did not. For this, Boltzmann’s memoirs are usually ascribed to classical statistical mechanics. Agreeing with Bach, it is shown that Boltzmann’s 1868 and 1877 calculations can lead to a Planckian distribution function, where those of 1868 are even closer to Planck than that of 1877. Boltzmann’s and Planck’s calculations are compared based on Bach’s three-level scheme ‘configuration–occupation–occupancy’. Special attention is paid to the concepts of interchangeability and the indistinguishability of particles and states. In contrast to Bach, the level of exposition is most elementary. I hope to make Boltzmann’s work better known in English and to remove misunderstandings in the literature.

Ring-Polymer Quantization of Photon Field in Polariton Chemistry

We use the ring-polymer (RP) representation to quantize the radiation field inside an optical cavity to investigate polariton quantum dynamics. Using a charge transfer model coupled to an optical cavity, we demonstrate that the RP quantization of the photon field provides accurate rate constants of the polariton mediated electron transfer (PMET) reaction compared to the Fermi's Golden rule. Because RP quantization uses extended phase space to describe the photon field, it significantly reduces the computational costs compared to the commonly used Fock states description of the radiation field. Compared to the other quasi-classical descriptions of the photon field, such as the classical Wigner model, the RP representation provides a much more accurate description of the polaritonic quantum dynamics, because it properly preserves the quantum distribution of the photonic DOF throughout the quantum dynamics propagation of the molecule-cavity hybrid system, whereas the classical Wigner model fails to do so. This work demonstrates the possibility of using the ring-polymer description to treat the quantized radiation field in polariton chemistry, offering an accurate and efficient approach for future investigations in cavity quantum electrodynamics.

Ring-Polymer Quantization of Photon Field in Polariton Chemistry

We use the ring-polymer (RP) representation to quantize the radiation field inside an optical cavity to investigate polariton quantum dynamics. Using a charge transfer model coupled to an optical cavity, we demonstrate that the RP quantization of the photon field provides accurate rate constants of the polariton mediated electron transfer (PMET) reaction compared to the Fermi's Golden rule. Because RP quantization uses extended phase space to describe the photon field, it significantly reduces the computational costs compared to the commonly used Fock states description of the radiation field. Compared to the other quasi-classical descriptions of the photon field, such as the classical Wigner model, the RP representation provides a much more accurate description of the polaritonic quantum dynamics, because it properly preserves the quantum distribution of the photonic DOF throughout the quantum dynamics propagation of the molecule-cavity hybrid system, whereas the classical Wigner model fails to do so. This work demonstrates the possibility of using the ring-polymer description to treat the quantized radiation field in polariton chemistry, offering an accurate and efficient approach for future investigations in cavity quantum electrodynamics.

ON QUANTUM CRYPTOGRAPHY

In the late twentieth century, human race entered the era ofinformation technology (IT). The IT industry, which deals with the production,processing, storage and transmission of information, has become an integralpart of the global economic system, a completely independent and significantsector of the economy. The dependence of the modern society on informationtechnologies is so great that omissions in information systems may lead tosignificant incidents. Telecommunications are the key information technologyindustry. However, information is very susceptible to various types of abuseduring transmission. The units for data storage and processing can bephysically protected from anyone wishing harm, but this does not hold truefor the communication lines that span hundreds or thousands of kilometersand are virtually impossible to protect. Therefore, the problem of informationprotection in the field of telecommunications is highly significant. Cryptology,particularly cryptography, deals with this issue. Quantum cryptography is arelatively new field ensuring safe communication between the sender and therecipient using the laws of quantum physics. This paper seeks to address theprinciples of the quantum distribution of a key for information encryption andthe fundamental problems arising from the execution.

Entangled Photon Source of Quantum Key Generator from Micro Ring Resonator for QKD Use

The powerful novel invention of entangled photon source by using a nonlinear silica micro ring resonator for quantum cryptography use was established and investigated. This entangled photon pair was generated under the degenerated four wave mixing process under the phase mismatch adjusment. The corresponding entangled photon generation Hamiltonian was established and studied in term of EPR pair. The obtained entangled photon pairs can be applied to the quantum cryptography distribution under quantum teleportation process showing the feasible and suitable for quantum information communication via the high visibility and $Q$ factor results. The advantage of this novel entangled photon source will be proved to become a part of quantum distribution device in the near future.

Quantum Distribution of a Sudoku Key

Sudoku grids are often cited as being useful in cryptography as a key for some encryption process. Historically transporting keys over an alternate channel has been very difficult. This article describes how a Sudoku grid key can be secretly transported using quantum key distribution methods whereby partial grid (or puzzle) can be received and the full key can be recreated by solving the puzzle.