Study On The Mechanism Of Quantum Friction In Several Typical Microscopic Systems

Friction in micro-scale is a typical problem in non-equilibrium statistical physics.Because the non-equilibrium statistical theory has not formed a sufficiently universal paradigm and the relevant theoretical tools are not mature enough,the research on micro scale friction is an open problem.There is no universal theory to describe and explain the energy dissipation mechanism in the friction process of micro system.Therefore,the study of micro scale friction has important theoretical significance.The research content of this paper is divided into four parts,namely,a."Metal surface-metal probe" system;b."Ferromagnetic surface-magnetic probe"system;c."Metal surface-vacuum-metal surface" system and d."NLSM-NLSM"system.The details are as follows:a.The model consists of a nano-scale electrically neutral probe and a metal surface.The nano probe scans the metal surface at a constant speed parallel to the metal surface.There is an interaction of exchanging electrons between the probe and the metal surface,and the existence of the probe causes the electrons on the metal surface to be affected by a potential,which is called surface potential.Firstly,we calculate the quantum action,and connect the imaginary part caused by the scanning speed with the dissipation of the system,and then calculate the friction based on this.The results show that the friction force on the probe is proportional to the scanning speed when the scanning speed is small,that is,linear friction;When the scanning speed is greater than a certain threshold,the dependence of friction on speed begins to become nonlinear.Finally,we discuss this result at a classical level.b.The quantum dissipation dynamics of a ferromagnetic surface scanned by a magnetic probe at a uniform speed,and the relationship between the friction force on the probe and the scanning speed are studied.The magnetic surface is parameterized as an XXZ model,while the magnetic probe is parameterized as a separate quantum spin M.The magnetic surface and the magnetic probe are coupled together by local magnetic exchange.In addition,the probe induces a surface potential acting on the quantum spin on the magnetic surface.All internal degrees of freedom are accumulated in the vacuum holding amplitude path integral formula of the system,and the quantum action is obtained.Based on this,the friction between the probe and the magnetic surface is calculated.The results show that when the relative velocity approaches zero,the imaginary part of the quantum action is suppressed,which means that the dissipation effect is very weak;Before the relative velocity reaches a certain value,the friction has a linear relationship with the relative velocity,and then the dependence of friction on velocity begins to show nonlinearity.c.The dissipation effect between two metal plates moving in parallel relative motion is studied.We model the interaction electron in the metal plate as an plasmon,which is linearly coupled with the vacuum fluctuation field in the gap between the two metal plates.We use an effective field theory to describe the plasmon,in which the plasmon corresponds to a scalar field.According to the order of perturbation expansion,a series of effective quantities of scalar field can be obtained,in which the simple harmonic approximation gives a colorless scattered plasmon corresponding to a quantum harmonic oscillator.The next-order perturbation gives a propagating plasmon,corresponding to a mass scalar field theory.We write the vacuum holding amplitude of the system as a path integral,and accumulate all the internal degrees of freedom to obtain the quantum action.The existence of relative motion leads to the vacuum instability of the system.Therefore,there is an imaginary part of the quantum action that depends on the relative motion speed,and its physical meaning is the probability of the simplest vacuum decay process.We associate it with the dissipation process,and calculate the friction between the two metal plates.For dispersionless plasmons,the imaginary part of the quantum action is strongly depressed at v→0,which indicates that the dissipation effect is not obvious when the relative motion speed is not large enough.The friction between plates is also strongly depressed as v→ 0.The difference from the imaginary part of quantum action is that the friction has a maximum with the increase of relative velocity.For dispersive plasmons,there is a relative velocity threshold of v=2γ.Only when the relative velocity reaches this threshold,the imaginary part of the quantum friction and friction begin to change from zero to non-zero.We give a semiclassical discussion on this,that is,as long as there is elementary excitation on the metal plates,this threshold will exist.Our numerical results also agree with this threshold.d.Two 1+2d O(3)symmetric NLSMs at zero temperature are considered.The two NLSMs are placed parallel to each other.We use Rand lto distinguish themL-NLSM is stationary in the laboratory coordinate system,while R-NLSM moves parallel to the two NLSM directions.The internal degrees of freedom in RNLSM,that is,quantum spin,are coupled with the internal degrees of freedom in L-NLSM through a nonlocal potential.In addition,we assume that the two nlsms are close enough that the distance between them can be recognized as zero,but their lattices are not in contact with each other,so the influence of lattice vibration can be ignored.Firstly,the nonlinear constraints of NLSM are treated by the mean field approximation through the vacuum holding amplitude of the system,and the effective action of the system is obtained.Secondly,taking the effective action as the starting point,we calculate the vacuum holding amplitude of the system,and then get the quantum action of the system.Thirdly,we make a boost transformation to R-NLSM to make it move,so that the vacuum of the system is no longer stable and the internal degrees of freedom of the system are excited.Finally,we calculate the imaginary part of the quantum action and associate it with the probability of vacuum decay of the system,and then calculate the internal friction of the system.The numerical results show the intuitive dependence of the imaginary part of quantum action and friction on the relative motion speed.It can be seen that there is a threshold of relative motion speed of 2u.Only when the relative motion speed is greater than this threshold,the imaginary part of quantum action and friction are not zero,which shows that only when this speed threshold is reached,quasi particles will be excited,the system will have dissipation and friction.We give a semiclassical discussion on this velocity threshold.