This book is based on the results of our interest in the ?eld of ultrashort laser pulses interaction with matter. The aim of our monograph was to build the balanced description of the thermal transport phenomena generated by laser pulses shorter than the characteristic relaxation time. In the book we explore the matter on the quark, nuclear as well atomic scales. Also on the cosmic scale (Planck Era) the thermal disturbance shorter than the Planck time creates the new picture of the Universe. The mathematics, especially PDE, are the main tool in the description of the ultrashort thermal phenomena. Two types of the PDE: parabolic and hyperbolic partial di?erential equations are of special interest in the study of the thermal processes. We assume a moderate knowledge of basic Fourier and d'Alembert eq- tions. The scope of the book is deliberately limited to the background of the quantum mechanics equations: Schr] odinger and Klein-Gordon. In this book the attosecond laser pulses are the main source of the dist- bance of the thermal state of the matter. Recently, the attosecond laser pulses constitute a novel tool for probing processes taking place on the time scale of electron motion inside atoms. The research presented in this book appears to provide the basic tools and concepts for attosecond thermal dynamics. Nevertheless much research is still needed to make this emerging ?eld routinely applicable for a broad range of processes on atomic and subatomic scales."

This book is based on the results of our interest in the ?eld of ultrashort laser pulses interaction with matter. The aim of our monograph was to build the balanced description of the thermal transport phenomena generated by laser pulses shorter than the characteristic relaxation time. In the book we explore the matter on the quark, nuclear as well atomic scales. Also on the cosmic scale (Planck Era) the thermal disturbance shorter than the Planck time creates the new picture of the Universe. The mathematics, especially PDE, are the main tool in the description of the ultrashort thermal phenomena. Two types of the PDE: parabolic and hyperbolic partial di?erential equations are of special interest in the study of the thermal processes. We assume a moderate knowledge of basic Fourier and d'Alembert eq- tions. The scope of the book is deliberately limited to the background of the quantum mechanics equations: Schr] odinger and Klein-Gordon. In this book the attosecond laser pulses are the main source of the dist- bance of the thermal state of the matter. Recently, the attosecond laser pulses constitute a novel tool for probing processes taking place on the time scale of electron motion inside atoms. The research presented in this book appears to provide the basic tools and concepts for attosecond thermal dynamics. Nevertheless much research is still needed to make this emerging ?eld routinely applicable for a broad range of processes on atomic and subatomic scales."

Fascinating developments in optical pulse engineering over the last 20 years lead to the generation of laser pulses as short as few femtosecond, providing a unique tool for high resolution time domain spectroscopy. However, a number of the processes in nature evolve with characteristic times of the order of 1 fs or even shorter. Time domain studies of such processes require at first place sub-fs resolution, offered by pulse depicting attosecond localisation. The generation, characterisation and proof of principle applications of such pulses is the target of the attoscience. In this book the interaction of the attosecond laser pulses with matter is investigated. The Proca's termal equation for laster - matter interaction is formulated and solved. It is shown that for attosecond laster pulses the Proca's thermal equation can be simplified and thermal Klein-Gordon equation is obtained. The book is divided into six chapters and the Epilogue presents the contemporary status of the attoscience: sub-femtosecond laster-matter interactions, master equations: Proca and Klein-Gordon equations and the perspectives: Attosecond Free Electron Laser (AFEL), LASETRON and Entangled Photon Laser (EPL).

Recent developments in the ultra-short laser technology and physics, especially at the attosecond time scale, open up new research frontiers for attoscience. This book examines the theoretical model for attophysics. The interaction of the attosecond laser pulses with slices of matter-attosecond tomography enables the description of the motion of electrons in atoms, molecules and 1D medium-graphene. The standard theory of the laser pulse-matter interaction is based on the parabolic Schrodinger equation, which leads to unphysical, infinite velocity of the thermal energy propagation. In this book, the Schrodinger equation is generalised to hyperbolic partial differential equation with finite velocity.