We extend a perturbative Dyson-type treatment and discrete-symmetry constraints from the Schrödinger and von Neumann equations to a dephasing Lindblad framework. This work develops further the odd-symmetric formulation involving dual temporal conditions from general dynamical considerations to specific tools of quantum mechanics. Applying the resulting scaling relations to published single- and double-diffractive data in $pp$ and $p\bar{p}$ collisions (ISR, UA4, UA5, CDF, D0, ALICE, and E710), we show that single-diffraction cross sections are well described by a three-parameter fit with a relative RMS deviation of $\sim 4\%$, substantially improving upon conventional approximations that neglect decoherence. The extracted decoherence factor is consistently $φ\approx 0.89$, in agreement across SD, DD, and E710-based (direct) estimates, and is naturally interpreted as $φ=1$ for CP-invariant dephasing but $φ<1$ for CPT-invariant dephasing, favouring the latter.
We extend a perturbative Dyson-type treatment and discrete-symmetry constraints from the Schrödinger and von Neumann equations to a dephasing Lindblad framework. This work develops further the odd-symmetric formulation involving dual temporal conditions from general dynamical considerations to specific tools of quantum mechanics. Applying the resulting scaling relations to published single- and double-diffractive data in pp and ppˉ collisions (ISR, UA4, UA5, CDF, D0, ALICE, and E710), we show that single-diffraction cross sections are well described by a three-parameter fit with a relative RMS deviation of ∼4%, substantially improving upon conventional approximations that neglect decoherence. The extracted decoherence factor is consistently φ≈0.89, in agreement across SD, DD, and E710-based (direct) estimates, and is naturally interpreted as φ=1 for CP-invariant dephasing but φ<1 for CPT-invariant dephasing, favouring the latter.
In the ordered phase of a Z2-symmetric collective spin system, two natural bases -- localised pointer states {∣P⟩,∣R⟩} and energy eigenstates {∣E0⟩,∣E1⟩} -- yield Lindblad dephasing rates that differ by a factor approaching 2 as N→∞ and reaching 2.42 near the quantum-critical crossover. The discrepancy has a single algebraic origin: parity forces ⟨Ei∣J^z∣Ei⟩=0 exactly, eliminating the cross-term that doubles the localised-state rate. Two distinct protection factors are identified: ηMF=(Nm∗)2/(2G01)≈2.42, where m∗ is the order parameter and G01=21(⟨E0∣J^z2∣E0⟩+⟨E1∣J^z2∣E1⟩) (advantage over the classical mean-field estimate), and ηexact=(G01+J012)/G01≈1.86, where J01=⟨E0∣J^z∣E1⟩ (exact physical ratio of pointer-state to eigenstate decay rate). In the thermodynamic limit the secular approximation fails, the doublet degenerates, and both rates converge. The three-regime structure is demonstrated in the Lipkin-Meshkov-Glick model via exact diagonalisation, and the algebraic origin of the discrepancy is established via the Z2 parity of the Lindblad jump operator.
In this work, the Dyson's equation formalism is outlined and applied toseveral open quantum systems. These systems are composed of a core,quantum-mechanical set of discrete states and several continua, representing macroscopic systems. The macroscopic systems introducedecoherence, as well as allowing the total particlenumber in the system to change.Dyson's equation, an expansion in terms of proper self-energy terms, isderived. The hybridization of two quantum levelsis reproduced in this formalism, and it is shown that decoherence followsnaturally when one of the levels is replaced by a continuum.The work considers three physical systems in detail. The first,quantum dots coupled in series with two leads, is presented in a realistic two-level model. Dyson's equation is used to account for the leads exactly to all ordersin perturbation theory, and the time dynamics of a single electron in the dotsis calculated. It is shown that decoherence from the leads damps the coherentRabi oscillations of the electron. Several regimes of physical interest areconsidered, and it is shown that the difference in couplings of the two leadsplays a central role in the decoherence processes.The second system relates to the decay-out ofsuperdeformed nuclei. In this case, decoherence is provided by coupling to theelectromagnetic field. Two, three, and infinite-level models are consideredwithin the discrete system. It is shown that the two-level model is usuallysufficient to describe decay-out for the classic regions of nuclearsuperdeformation. Furthermore, a statistical model for the normal-deformedstates allows extraction of parameters of interest to nuclear structure fromthe two-level model. An explanation for the universality of decayprofiles is also given in that model.The final system is a proposed small molecular transistor. TheQuantum Interference Effect Transistor is based on a single monocyclic aromatic annulene molecule, with twoleads arranged in the meta configuration. This device is shown to be completely opaque to charge carriers, due to destructive interference. Thiscoherence effect can be tunably broken by introducing new paths with a real orimaginary self-energy, and an excellentmolecular transistor is the result.
CP bias in proton--antiproton diffractive dissociation can be viewed from several philosophical perspectives, notably stochastic realism and stochastic epistemicism. When combined with the presumption of temporal symmetry, stochastic realism suggests that the laws of physics allow the possibility of thermodynamic antisystems, although whether antisystemic characteristics can be physically realised in nature remains an open question.
Here, this bias is interpreted as apparent, indicating significant non-unitary contributions and a distinction from fundamental CP violations arising from unitary Hamiltonian dynamics. Such apparent effects may arise from intrinsic stochasticity, from environmental interactions, or from interference between the two. This work investigates the relevant mechanisms and determines conditions for creating, transmitting, or screening a CP bias.
In the environmental branch, an equilibrated radiation bath may transmit a CP bias from matter-dominated surroundings, although causality constraints may limit this possibility. In the intrinsic branch, the observed bias is consistent with subleading antisystemic effects required by CPT invariance. Further experiments are needed to distinguish between these mechanisms.
The act of measurement on a quantum state is supposed to "dephase" (dephasing refers to the phenomenon that the states lose phase coherence; then the phases get randomized in interaction with a bath of other oscillators, which is referred to as "decoherence"), then "decohere" and "collapse" (or more precisely "register" and "reduce") the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside standard quantum-mechanical evolution and not calculable from Schrödinger's equation. Progress has, however, been made in studying this problem with two main calculation tools-one uses a time-independent Hamiltonian, while a rather more general approach proving that decoherence occurs under some generic conditions. The two general approaches to the study of wave-function collapse are as follows. The first approach, called the "consistent" or "decoherent"' histories approach, studies microscopic histories that diverge probabilistically and explains collapse as an event in our particular history. The other, referred to as the "environmental decoherence" approach studies the effect of the environment upon the quantum system, to explain wave-function decoherence which is produced by irreversible effects of various sorts. However, as we know, wave-function collapse is not related to thermal connection with the environment, rather, it is inherent to how measurements are performed by macroscopic apparata. In the "environmental decoherence" approach, one studies decoherence using a Markovian-approximated Master equation to study the time-evolution of the reduced density matrix (post dephasing) and obtains the long-time dependence of the off-diagonal elements of this matrix. The calculation in this paper studies the evolution of a quantum system starting with "dephasing" followed by the effects of the environment with some differences from prior analyses. We start from the Schrödinger equation for the state of the system, with a time-dependent Hamiltonian that reflects the actual microscopic interactions that are occurring. Then we systematically solve (exactly) for the time-evolved state, without invoking a Markovian approximation when writing out the effective time-evolution equation, i.e., keeping the evolution unitary until the end. This approach is useful, and it shows that the system wave-function will explicitly "un-collapse" if the measurement apparatus is sufficiently small. However, in the limit of a macroscopic system, this "dephasing" quickly leads to "decoherence"-collapse is a temporary state that will simply take extremely long (of the order of multiple universe lifetimes) to reverse. This has been attempted previously and our calculation is particularly simple and calculable. We make some connections to the work by Linden et al. while doing so. The calculation in this paper has interesting implications for the interpretation of the Wigner's friend experiment, as well as the Mott experiment, which is explored in "Connection to some general theoretical results" and "Recurrence times" (especially the enumerated points in "Recurrence times"). The upshot is that as long as Wigner's friend is macroscopically large (or uses a macroscopically large measuring instrument), no one needs to worry that Wigner would see something different from his friend. Indeed, Wigner's friend does not even need to be conscious during the measurement that she conducts. It also allows one to reasonably interpret some of the more recent thought experiments proposed. In particular, as a result of the mathematical analysis, the short-time behavior of a collapsing system, at least the one considered in this paper, is not exponential. Instead, it is the usual Fermi-golden rule result. The long-term behavior is, of course, still exponential. This is a second novel feature of the paper-we connect the short-term Fermi-golden rule (quadratic-in-time behavior) transition probability to the exponential long-time behavior of a collapsing wave-function in one continuous mathematical formulation.
We describe the effect of pure dephasing upon the time-dependent dynamics of two-state quantum systems in the framework of a Lindblad equation for the time evolution of the density matrix. A uniform approximate formula is derived, which modifies the corresponding lossless transition probability by an exponential factor containing the dephasing rate and the interaction parameters. This formula is asymptotically exact in both the diabatic and adiabatic limits; comparison with numerical results shows that it is highly accurate also in the intermediate range. Several two-state models are considered in more detail, including the Landau-Zener, Rosen-Zener, Allen-Eberly, and Demkov-Kunike models, along with several other models, such as a Gaussian model and a Landau-Zener model with a pulsed coupling.
We develop a derivation of dynamics of Quantum Mechanics and measurement within a fundamentally timeless and scale-invariant framework. Building on a prior reconstruction of quantum kinematics from renormalization consistency, we extend the analysis to dynamical evolution and the measurement process using three minimal principles: a global constraint (timelessness), a variational formulation, and resolution independence. We show that relational time emerges through conditional decomposition of the global state, leading to an effective Schrödinger evolution under suitable conditions on clock subsystems. Renormalization group (RG) transformations, treated as maps on the state space induced by coarse-graining, generate an effective non-unitary dynamics for reduced states. Under standard assumptions of weak coupling and scale separation, this dynamics takes Lindblad form, providing a structural origin for decoherence. A central result of this work is the formulation of a stability selection principle: configurations contributing to observable physics correspond to those that are simultaneously stationary under the action and stable under RG flow. This principle unifies dynamical selection (via the variational structure) and structural selection (via renormalization), and provides a mechanism for the emergence of classical behavior. Measurement is described as an effective sector dynamics arising from decoherence and coarse-grained evolution. The Lindblad equation admits a stochastic representation in which the system evolves between dynamically independent sectors, leading to an effective description of definite outcomes without introducing a fundamental collapse postulate. The Born rule follows from the unique quadratic measure consistent with refinement structure and is realized dynamically within this framework. Together, these results provide a structural account under minimal assumptions of quantum dynamics, decoherence, and measurement as emergent features of a timeless, renormalization-consistent theory governed by stability across scales.