Decoherence of quantum states in QCD vacuum
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coherence of Quantum States in QCD Vacuum V. Kuvshinov* and E. Bagashov Joint Institute for Power and Nuclear Research–Sosny, National Academy of Sciences of Belarus, Minsk, 220109 Belarus *e-mail: [email protected] Abstract⎯The stochastic vacuum of quantum chromodynamics is used as an environment for quarks considered as color state vectors. It is shown that during interaction with the stochastic vacuum information of the quark color state is lost with time (decoherence of the quark state vector occurs), which effectively means that it is impossible to observe the quark as a free color particle (confinement). DOI: 10.1134/S1063779617050288
INTRODUCTION The interaction of a quantum system with an environment can be effectively described by adding stochastic terms to the Hamiltonian of the system. In this case, the system density matrix is obtained by averaging over the degrees of freedom of the environment. Interaction with the environment leads to decoherence and disappearance of quantum superpositions. After a rather long period of time, information on the initial state of the quantum system is lost. Quantum decoherence is the loss of coherence or ordering of phase shifts between the constituents of the system in the quantum superposition. Decoherence results from the thermodynamically irreversible interaction of the system with the environment. This process can be regarded as the loss of information [1]. 1. STOCHASTIC QCD VACUUM The model of the stochastic vacuum of quantum chromodynamics considers only field correlators of no higher than second order [2] (Gaussian dominance). This model is verified by the lattice calculations [3]. One of its important consequences is the Casimir scaling [4]. The model is based on the assumption that vacuum expectation values of gauge-invariant quantities can be calculated as expectation values with respect to some “well-behaved” stochastic gauge field. It is known that such a vacuum leads to confinement, generating QCD strings with constant tension on the large-distance asymptotics. We will consider the stochastic QCD vacuum as an environment for color quantum particles and perform averaging over its degrees of freedom instead of considering nonperturbative dynamics of Yang–Mills fields. As a result, we arrive at the decoherence of the quark state, relaxation of quantum superpositions, loss of
information, and color confinement, ultimately having colorless objects described by the density matrix. 2. PARTICLE–VACUUM INTERACTION As is shown in [5], propagation of a spinless heavy particle in the stochastic QCD vacuum along path γ can be described by the expression
ρˆ f = N c−1 + (ρˆ in − N c−1)W adj(γ),
(1)
where ρˆ in and ρˆ f are the density matrices of the initial and final states respectively, N c is the number of colors, and W adj is the Wilson loop [6] in the adjoint representation. This expression was obtained by averaging solutions of transport equations in degrees of freedom of the vacuum (i.e., by functional integration over field variables). Considering that t
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