Understanding Quantum Dissipation from an Energy Distribution Perspective:Universal Formulas for Internal Dissipation Power and the Energy Distribution Ratio f, and a Generalization of the Fluctuation-Dissipation Theorem

Ende Guo

Feb 23, 20260 citations

Secrecy Outage Minimization for Wireless Powered Communication Networks with an Energy Harvesting Jammer

Jihwan Moon, Hoon Lee, Changick Song +1 more

GlobecomDec 1, 201612 citations

Optics Express

Quantum analog of the maximum power transfer theorem

Cristian L. Cortes, Wenbo Sun, Zubin Jacob

Published Aug 31, 2022• 1 citation

Publisher

Abstract

DOI: 10.1364/oe.465020

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Quantum maximum power transfer theorem

Cortes, Cristian L., Zubin Jacob

We discover the quantum analog of the well-known classical maximum power transfer theorem. Our theoretical framework considers the continuous steady-state problem of coherent energy transfer through an N-node bosonic network coupled to an external dissipative load. We present an exact solution for optimal power transfer in the form of the maximum power transfer theorem known in the design of electrical circuits. We provide analytical expressions for both the maximum power delivered to the load as well as the energy transfer efficiency which are exact analogs to their classical counterparts. Our results are applicable to both ordered and disordered quantum networks with graph-like structures ranging from nearest-neighbour to all-to-all connectivities. This work points towards universal design principles which adapt ideas of power transfer from the classical domain to the quantum regime for applications in energy-harvesting, wireless power transfer, energy transduction, as well as future applications in quantum power circuit design.We discover the quantum analog of the well-known classical maximum power transfer theorem. Our theoretical framework considers the continuous steady-state problem of coherent energy transfer through an N-node bosonic network coupled to an external dissipative load. We present an exact solution for optimal power transfer in the form of the maximum power transfer theorem known in the design of electrical circuits. We provide analytical expressions for both the maximum power delivered to the load as well as the energy transfer efficiency which are exact analogs to their classical counterparts. Our results are applicable to both ordered and disordered quantum networks with graph-like structures ranging from nearest-neighbour to all-to-all connectivities. This work points towards universal design principles which adapt ideas of power transfer from the classical domain to the quantum regime for applications in energy-harvesting, wireless power transfer, energy transduction, as well as future applications in quantum power circuit design.

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The transfer of a quantum state between distant nodes in two-dimensional networks is considered. The fidelity of state transfer is calculated as a function of the number of interactions in networks that are described by regular graphs. It is shown that perfect state transfer is achieved in a network of size $N$ , whose structure is that of an $(N∕2)$ -cross polytope graph, if $N$ is a multiple of $4$ . The result is reminiscent of the Babinet principle of classical optics. A quantum Babinet principle is derived, which allows for the identification of complementary graphs leading to the same fidelity of state transfer, in analogy with complementary screens providing identical diffraction patterns.The transfer of a quantum state between distant nodes in two-dimensional networks is considered. The fidelity of state transfer is calculated as a function of the number of interactions in networks that are described by regular graphs. It is shown that perfect state transfer is achieved in a network of size $N$, whose structure is that of an $(N∕2)$-cross polytope graph, if $N$ is a multiple of $4$. The result is reminiscent of the Babinet principle of classical optics. A quantum Babinet principle is derived, which allows for the identification of complementary graphs leading to the same fidelity of state transfer, in analogy with complementary screens providing identical diffraction patterns.

arXiv:0808.2261Physical Review ADec 5, 200818 citations

Ende Guo

Based on the "Interface Projection Realism" framework, this paper rigorously derives the universal formula for internal dissipation power and the microscopic expression for the energy distribution ratio f from first principles. We treat the qubit (Q), the interfacial defect network (D), and the bulk dissipation channel (B) as a self-contained total system, no longer presupposing any part of it as an external environment. By applying the Born-Markov approximation to the degrees of freedom of D and B, we obtain the reduced master equation for Q, and subsequently calculate the net energy flow rate from Q to the incoherent degrees of freedom—the internal dissipation power R_internal. The result is: R_internal = ħω_q [Γ↓ ⟨n⟩ - Γ↑ (1-⟨n⟩)], where Γ↓ and Γ↑ are transition rates determined by the Q-D coupling and the internal structure of D, and ⟨n⟩ is the excited state population of Q. This formula does not rely on any thermal equilibrium assumptions and is applicable to arbitrary Markovian non-equilibrium steady states. Building on this, we define the total effective power absorbed by the system as R_total = ⟨∂H_drive/∂t⟩ and introduce the system's stored energy E_stored = ⟨H_Q⟩. Under periodic averaging, the energy conservation equation reads dE_stored/dt = R_total - R_internal, where the overline denotes time average. The energy distribution ratio f = R_internal / R_total satisfies f = 1 in the periodic steady state where dE_stored/dt = 0; during transients, f can deviate from 1, its specific expression depending on microscopic parameters, reflecting the degree of deviation from the steady state. We further demonstrate that when D and B are in thermal equilibrium, the above formula reduces to the traditional fluctuation-dissipation theorem. This paper proves that the universal formula for internal dissipation power naturally contains the fluctuation-dissipation theorem under thermal equilibrium conditions, while its validity in non-equilibrium states constitutes a non-equilibrium generalization of the traditional theorem, providing a unified theoretical foundation for understanding the energetic origin of quantum decoherence.Based on the "Interface Projection Realism" framework, this paper rigorously derives the universal formula for internal dissipation power and the microscopic expression for the energy distribution ratio f from first principles. We treat the qubit (Q), the interfacial defect network (D), and the bulk dissipation channel (B) as a self-contained total system, no longer presupposing any part of it as an external environment. By applying the Born-Markov approximation to the degrees of freedom of D and B, we obtain the reduced master equation for Q, and subsequently calculate the net energy flow rate from Q to the incoherent degrees of freedom—the internal dissipation power R_internal. The result is: R_internal = ħω_q [Γ↓ ⟨n⟩ - Γ↑ (1-⟨n⟩)], where Γ↓ and Γ↑ are transition rates determined by the Q-D coupling and the internal structure of D, and ⟨n⟩ is the excited state population of Q. This formula does not rely on any thermal equilibrium assumptions and is applicable to arbitrary Markovian non-equilibrium steady states. Building on this, we define the total effective power absorbed by the system as R_total = ⟨∂H_drive/∂t⟩ and introduce the system's stored energy E_stored = ⟨H_Q⟩. Under periodic averaging, the energy conservation equation reads dE_stored/dt = R_total - R_internal, where the overline denotes time average. The energy distribution ratio f = R_internal / R_total satisfies f = 1 in the periodic steady state where dE_stored/dt = 0; during transients, f can deviate from 1, its specific expression depending on microscopic parameters, reflecting the degree of deviation from the steady state. We further demonstrate that when D and B are in thermal equilibrium, the above formula reduces to the traditional fluctuation-dissipation theorem. This paper proves that the universal formula for internal dissipation power naturally contains the fluctuation-dissipation theorem under thermal equilibrium conditions, while its validity in non-equilibrium states constitutes a non-equilibrium generalization of the traditional theorem, providing a unified theoretical foundation for understanding the energetic origin of quantum decoherence.

Feb 23, 20260 citations

Secrecy Outage Minimization for Wireless Powered Communication Networks with an Energy Harvesting Jammer

Jihwan Moon, Hoon Lee, Changick Song +1 more

In this work, we consider a wireless powered communication network (WPCN) with an energy harvesting (EH) jammer where an eavesdropper tries to wiretap the communication between a user and a hybrid access-point (H-AP). In our system, the H-AP first transmits an energy signal to recharge the batteries of the EH user and the EH jammer in the energy transfer (ET) phase. Then, in the subsequent information transfer (IT) phase, the user sends its information signal to the H-AP, while the jammer generates the jamming signal to interfere the eavesdropper utilizing the harvested energy in the ET phase. Assuming only the channel distribution information (CDI) of the eavesdropper is available at the legitimate nodes, we analyze and minimize the secrecy outage probability by optimizing the time allocation between the two phases. To reduce the complexity, we also provide a simple closed-form solution, and the simulation results verify that its performance approaches the optimum.In this work, we consider a wireless powered communication network (WPCN) with an energy harvesting (EH) jammer where an eavesdropper tries to wiretap the communication between a user and a hybrid access-point (H-AP). In our system, the H-AP first transmits an energy signal to recharge the batteries of the EH user and the EH jammer in the energy transfer (ET) phase. Then, in the subsequent information transfer (IT) phase, the user sends its information signal to the H-AP, while the jammer generates the jamming signal to interfere the eavesdropper utilizing the harvested energy in the ET phase. Assuming only the channel distribution information (CDI) of the eavesdropper is available at the legitimate nodes, we analyze and minimize the secrecy outage probability by optimizing the time allocation between the two phases. To reduce the complexity, we also provide a simple closed-form solution, and the simulation results verify that its performance approaches the optimum.

GlobecomDec 1, 201612 citations

N

, whose structure is that of an

(N∕2)

-cross polytope graph, if

N

is a multiple of

4

. The result is reminiscent of the Babinet principle of classical optics. A quantum Babinet principle is derived, which allows for the identification of complementary graphs leading to the same fidelity of state transfer, in analogy with complementary screens providing identical diffraction patterns.